Our instincts have evolved in situations where copies did not exist, so taking a bullet in one's head was always a loss. Regardless of what thought experiments you propose, my insticts will still reject the premises and assume that copies don't exist and that the information provided to me is false.

If copying would be a feature in our ancient environment, organisms who took the bullet if it saved e.g. two of their copies would have an evolutionary advantage. So their descendants would still hesitate about it (because the information that it will save their two copies could be false; and even if it is right, it would still be better to spend some time looking for a solution that might solve all three copies), but ultimately many of them would accept the deal.

I'm not sure what is the conclusion here. On one hand, the fact that some hypothetical other species would have other values doesn't say much about our values. On the other hand, the fact that my instincts refuse to accept the premise of your thought experiment doesn't mean that the answer of my instincts is relevant for your thought experiment.