For sake of argument we say that the plant requires a rare and unstable isotope to get started. Earth's entire supply is contained in the plant and will decay in 24 hours.

I could also ask you a similar dilemma, but this time there is only one theory which acknowledges that whether the plant works or creates a black hole depends on a single quantum event, which has a 50% chance of going either way. What do you do? If you wouldn't launch I can ask the same question but now there's only a 25% chance of a black hole, and so on until I learn the ratio of the utility values that you assign to "post scarcity future" and "extinction of humanity". This might for example tell me that the chance of a black hole has to be less than 30% for you to press the button.

Then I ask you the original dilemma, and learn whether the probability you assign to theory X is above or below 70%. If I have far too much time on my hands I can keep modifying the dilemma with slightly altered pay-offs until I pinpoint your estimate.

This avoids the question. If it helps, try to construct a version of this in the least convenient possible world. For example, one obvious thing to do would be that something about theory X means the plant can only be turned on at a certain celestial conjunction (yes, this is silly but it gets the point across. That's why it is a least convenient world) and otherwise would need to wait a thousand years.

One can vary the situation. For example, it might be that under theory X, medicine A will save a terminally ill cancer patient, and under theory Y, medicine B will save them. And A and B together will kill the patient according to both theories.

To give a simple example, consider flipping a coin. You observe HHH. Is this a fair coin? or a double-headed one? or a biased coin? Different theories describe these situations, and you could be asked to bet on them. Imagine you then further observe HHHH - making a total of HHHHHHH. This makes your estimate of the chances of the "double-headed coin" hypothesis go up. Other hypotheses may increase in probability too - but we are not troubled by there being an infinity of them, since we give extra weight to the simpler ones, using Occam's razor.