Shrug I am a user of the site.
I think VtC is a serious decision/action. It should not be taken lightly.
What follows is my opinion, it may be in line with guidelines for SE or it may not.
It is my opinion, there should be levels of escalation.
1) You do not like the question, don't understand the question, prejudiced against the assertions made in the question etc. You can down vote the question and move on.
2) You think the question is ok, just not workable as in needing the questioner to redo it. You can flag the Question.
3) You are convinced the question is not correct for this Q/A and can not be salvaged. You can VtC.
At level 3 there should not be a take back. You had your reasons, they were carefully thought out and objectively executed. Others may agree with you, they may not agree with you.
You seem to want to change the "reason" you VtC'd from A to B. I make mistakes, I am human, this action is an action that should be taken seriously and that means you should be careful/deliberate,sure of the choices your making.
Edit to OP: "See edited question" - I did see the edited question. I am saying that Not being able to change your choice should be the cost of being able to Vote To Close. Why not flag it and put it on hold and suggest changes or give time to see others opinions?
Edit Rand al'Thor "Also, re point 2: flag it as what?" - Flag it using the flag that most characterizes your reasons. While I do not have access to the VtC process/reasons, one might ask why the VtC reasons do not show up for those that are able to VtC. For clarity, Leaving the Post in Hold but indicating the reason to close.
Edit Rand al'Thor "So I can't see any difference between your options 2 and 3; the only difference between flagging for closure and voting to close is in the reputation of the user doing it, not in the nature of the question" - Then perhaps the fact that Reputation is able to close based on a Flag is more of a hindrance than a feature. IF the flag does not close the question, then the OP could in fact execute the 2nd level before escalating to the 3rd level. Regardless there are other Flags that can be used that puts the post on Hold. OR i am simply not understanding what your point is.