Suppose a police officer has probable cause to arrest me, based on evidence in plain sight. He wants to initiate a search pursuant to arrest.
Before the officer can detain me, I put the (alleged) evidence in a place where it is accessible, but if accessed incorrectly the evidence is permanently destroyed (or rendered useless to a prosecution, etc.)
This wouldn't happen. The moment you are placed under arrest you are handcuffed and detained. Not only for officer safety, but also for that very reason (so you cannot destroy or secret away evidence).
The officer asks me to produce the evidence, and I refuse. Consider several scenarios:
- Do I have grounds to refuse to produce it because it would be incriminating; I am under no obligation to incriminate myself?
No. If the officer is searching you pursuant to arrest (and under your scenario he need not get a warrant as there is evidence in plain view, although he could begin cursory search and have a warrant executed and brought over within an hour, just to be safe). Regardless, you are not consulted as to whether it's OK or not, hence no right to refuse. Further, your 5th amendment right against self incrimination gives you the right not to answer, but you can expect your dwelling to be completely destroyed if they know there is evidence there. Since we are supposing: suppose you actually did get away from the police, before they cuffed you, and were able to get to evidence before being searched and without getting shot (unlikely). They would tear your place apart and would find it.
- The officer, perhaps not knowing the risk involved, attempts to retrieve the evidence and fails, causing the evidence to be destroyed. If the officer can show that I knowingly put the (alleged) evidence in such a situation and allowed him to destroy it, what might the repercussions be after the fact?
You would be charged with destruction of evidence, on top of whatever you were originally arrested for that they saw in plain view. Further, forensics would almost certainly find some trace of what you were hiding. This scenario is highly unlikely.
- The officer, perhaps understanding the risk, goes to a court and asks them to compel my cooperation. Could this happen and, if so, how?
The officer, if he knew it, would just find a way to get at it that wouldn't allow for its destruction. They can literally take out pieces of walls, pipes, whatever. They have the resources to get to anything. If the search would become unreasonable lest the Court knew of your dastardly plan, they would just expand the scope of the search via the warrant.
- Suppose I intend to cooperate but accidentally cause the evidence to be destroyed. What might the repercussions be for me, and who would bear the burden of proof?
Same result. You hid it. You destroyed it. You decided to potentially destroy it when you put it in that place, so the outcome is not different.
- Suppose the device has another function which produces some other items which are not incriminating. Suppose the officer retrieves these instead of the real evidence. Am I under any obligation to tell the officer whether those are the only items to be found, if I am hiding other items, etc.?
Your only obligation if you're being searched is to be quiet! You have no obligation to help, nor should you help, with the search of your property. But this is not something out of James Bond or Batman. What? Your secret device turns cocaine into sugar? Seriously, this wouldn't happen. If the police thought evidence to be in a place, they wouldn't stop looking because they found something innocuous. They would take whatever it's in apart revealing all its contents.
- Can the mere possession of such a device be used by the prosecution to show criminal intent (e.g., a crowbar, flashlight and ski mask in my trunk)?
What device? Now I'm really confused. If you are being searched on suspicion of burglary or robbery for example, the tools a burglar would use or if the robber wore a mask are all viable as potential evidence and would all be seized as such.