I wasn't one of those who voted to close the question, so I'm not really in a position to comment on their reasons for voting to close. What follows are my own opinions, please ignore any diamond you might see attached to my name!

I think the original version of the question was probably actually on-topic, but should have been worded better. The series of edits that followed is probably what made people think that you were arguing for a conspiracy theory, and suggested the topic would be a better fit for skeptics:SE.

You ask how can it be considered "conspiracy"?

Your thesis seems to be that the United States conspired with the Israeli government to cover up a deliberate attack on a US Navy vessel by the IDF. Further, your quotes are all sourced from a site that also argues the existence of a conspiracy and cover-up. If that is your thesis, then the question probably does belong on the Skeptics site.

In this instance, it's not a question of whether you locate the original quotes, it's a question of whether those quotes have been chosen selectively for that site, and whether they were taken within context.

It is also not a question of the positions that these people had formerly occupied. The question should be 'Do these people have any direct knowledge of the events in question". The statement:

"I feel the Israelis knew what they were doing. They knew they were shooting at a U.S. Navy ship"

means nothing. It isn't evidence one way or the other. What someone feels might have happened isn't evidence. Their former position is irrelevant unless it gave them access to specific information about the incident. Including comments like this in your question does make it look more like an argument for a conspiracy theory, and less like a history question.

The quotes

In fact, only three of your sources cited any information to support the claim that the attack was deliberate. Former US Ambassador to Lebanon Dwight Porter

"It's an American ship!" the pilot of an Israeli Mirage fighter-bomber radioed Tel Aviv as he sighted the USS Liberty on June 8, 1967. Israeli headquarters ordered the pilot to attack the American ship."

Lieutenant General William E. Odom, former director, National Security Agency:

"On the strength of intercept transcripts of pilots' conversations during the attack, the question of the attack's deliberateness "just wasn't a disputed issue" within the agency."

and Oliver Kirby, former deputy director for operations/production, National Security Agency:

"I can tell you for an absolute certainty (from intercepted communications) that they knew they were attacking an American ship."

You'll notice that all three cite the same source - intercepted radio communication from the IDF pilots.

However, when researching for my answer, it did not take me long to find a report in the Wall Street Journal of a 2001 letter from former Navy Chief Petty Officer Marvin Nowicki. He had been the chief Hebrew-language analyst aboard a U.S. Navy EC-121 spy plane that was intercepting Israeli aircraft communications during the attack on the USS Liberty.

He stated that he did indeed hear (and record) Israeli pilots’ and captains’ references to the U.S. flag flying on the deck of the Liberty, but that these remarks were made only after the attack was underway, and not before. Shockingly, that particular story does not appear to be quoted on the site you referenced.

You might very well think that is because it undermines their claim of a conspiracy. I, however, couldn't possibly comment.

Now, I can't speak for anyone else, but as an historical researcher I would always give far more weight to the testimony of an eyewitness than to that of someone who later saw a report about an incident - regardless of their respective ranks. The only reason an historian would ignore that evidence would be because it didn't support the conclusion they were trying to reach. And that is bad practice (not just in the study of history)!

The edit timeline

Like I said right at the start, I'm not one of the people who voted to close the question. However, looking at the timeline of edits I can see that the question was only closed after you'd gone through a series of edits to incorporate quotes taken from a site which, as I explained above, is attempting to prove a conspiracy.

Personally, I would not be surprised if that was a factor in at least some cases for deciding that the question was off-topic for this site. It may also be a factor in the impressive number of downvotes that the question has attracted.

So, could the original question have been written in a way that was on-topic for this site?

I think so. I'd suggest that the structure of a valid question could be:

1. A (very brief) description of the incident, with a link to a site for people who want to find out more. Try to find an unbiased site, or perhaps just Wikipedia.
2. Mention the declassified report from the Israeli Court of Enquiry. Now, if you are going to quote from the report, quote the text exactly as written. Do not attempt to improve their spelling or grammar, and do not paraphrase, as you have done in the question here. Also, be very careful to avoid the appearance of quoting selectively from the text. In the excerpt you've included here, for example, you chose to omit the evidence that 2 IDF officers on 2 different vessels apparently independently identified the ship as Egyptian. Whether or not that evidence was true, omitting it from your question, while including the later section from the bottom of page 5, creates the impression of bias. Generally, I would suggest that it is better in cases like this just to quote the conclusions, and let people read the whole document for themselves.
3. State that many survivors have never accepted the findings of the Israeli Court of Enquiry. State that their opinion seems to be shared by a number of former high ranking US officials. Provide a link to your site (as you did in the original version of the question) to support these assertions. Feel free to mention a few names, but there is no need to quote every one of them (or, indeed any of them) in your question. People can click the link and read for themselves.
4. Point out that the NSA has released hundreds of declassified documents since 1967, some of which directly relate to the incident.
5. Finally, ask whether there is any evidence amongst all the material declassified since 1967 to contradict the official version of events - i.e. that the attack was a mistake, resulting from poor communication between units of the IDF and the mis-identification of the vessel.

But that is just my opinion. Others may take a different view.

Editing questions with existing answers

I would also suggest that it is also worth bearing in mind that in response to another question here on meta, people expressed strong views about questions being edited in a way that then invalidates existing answers (I can't say for certain, but that may explain some of the downvotes you've received in this case).

Given that, I would suggest that in those circumstances it is worth asking a new question.

Your Questions

You have asked 2 questions (apart from your "Solicitations for Ideas"). I shall try to answer the second question first.

You new question, or "second wording" as you refer to it, is actually a very different question.

The new question:

"... what historical events had the most influence on relatively cool relations prior to 1967, and exponentially improving relations after 1967?"

bears almost no relation to the original question:

"Why did the Israeli Defense Force attack the USS Liberty on June 8, 1967 killing 32 American Sailors, wounding 171, and doing so much damage to the ship that it ultimately had to be scrapped."

Now, given the views expressed in the answers to the question I mentioned above, about questions being edited in a way that then invalidates existing answers, I suspect that we have the answer to your second question:

"Why can't we open the existing question given as written the original question asked for reasons for the attack, and was not about the attack itself. Both question dealt with events leading up to the attack?"

Because it is not the same question.

You should have asked a new question, rather than editing the original. Never mind the merits, or otherwise, of the new question, if people think that you should not have edited the question in the first place they probably won't vote to re-open.

Of course, I may be wrong. The answer may just be 42. (It's a messed-up Universe!)

Now, as to your first question, you asked whether the new question is more acceptable.

Personally, I see several problems with the new question as it stands. The most obvious of which are implicit assumption that US foreign aid to Israel was only contingent on events in the region and that you are quoting average figures over long periods of time which do not appear to reflect the detail in the table on the site from which you are quoting.

In the new question, you also appear to be claiming that the attack on the USS Liberty had a particular significance for US/Israeli relations without providing any clear evidence to support that assertion. Put simply, why would the USS Liberty attack on 8 June 8 1967 act as a fulcrum or pivot?

For me, you would need to add that supporting evidence to the question, or we are likely to be back to the conspiracy theory arguments.

For example, 1967 was also in the middle of a pivotal period in the Vietnam War and the build up of US forces there under President Johnson. Not to mention the small matter of the Tet Offensive in Vietnam in early 1968. Now, I don't lay claim to any particular inside knowledge, but it seems to me - in the absence of any new evidence - just as likely that the global situation, particularly in regard to the escalation in Vietnam, might have been the trigger for increased funding for America's main ally in the Middle East through the 1970s, and that the attack on the USS Liberty wasn't a factor at all.

So why do you think that the attack on the USS Liberty changed US foreign policy in 1967/68? What evidence are you offering in support of that position? Are there declassified papers that suggest that this was the case? Non-trivial assertions that are not supported by evidence are rarely well received on this site.

From what you have written, it seems that you have a particular answer that you believe to be correct. If that is indeed the case, you can post a new question and answer it yourself, but remember that the normal rules and guidance about asking and answering questions will still apply. It still needs to be on-topic for this site.

The Role of Moderators

Lastly, you have asked about moderator concerns.

At this point I'll put my moderator hat back on, but please bear in mind that I'm still just speaking for myself. Other moderators may interpret the guidance differently.

I think you misunderstand the role of moderators on Stack Exchange.

Personally, I am trying to exercise a "light-touch", in accordance with my reading of the Theory of Moderation, which explains that we are "human exception-handlers". Interpret that as you will!

As a moderator I can close or re-open questions with a single vote. However, just because I can doesn't mean that I should.

I've argued here on meta in the past that some questions have been closed when they shouldn't have been. I now have the power to re-open them. I haven't done so because I think that would be an abuse of that power. (In fact, now I can't even nominate them to be re-opened and let the community decide. As a moderator, if I vote to re-open, the question is just re-opened").

Except in particularly egregious cases (Nazi spammers, posts that are just 'vandalism', etc.), I prefer to let the community vote. If I do vote to close or re-open, the it will normally only be as the fifth (or, at a push, the fourth) vote.

If posts are flagged for moderator attention by members of the community then I, or one of my fellow moderators, will review the flag and decide accordingly.

What that means in the context of your question is that I will not normally override a decision to close a post by members of the community.

If you want to get a post that was closed by the community re-opened, you will need to convince the community that it should be re-opened. (If the post was closed by a moderator then there is a procedure available to you if you want us to reconsider the decision).