The trouble is that if the Collatz conjecture is true then {"Collatz conjecture is true"} constitutes an exhaustive set of outcomes, whose probability you think is only 1/2.

And if the Collatz conjecture is false then {"Collatz conjecture is false"} constitutes a single outcome, whose probability I think is 1/2. As of now I don't know which premise (if true, if false) is actually the case, so I represent my uncertainty about the premises with a probability of 0.5. Representing uncertainty about an outcome (even an outcome that we would know if we were logically omniscient) does not make you dutch-bookable; incorrectly determining your uncertainty makes you dutch-bookable.

"Should PB accept bet X that PB will reject bet X?"

Even easier. No. "I'll bet you a dollar you won't take this bet." "So if I take it, I lose a dollar, and if I don't take it, I lose nothing? I reject the bet. Having rejected the bet, you will now proceed to point out that I would have won the bet. I will now proceed to show you that taking the bet closes off the path where I win the bet (it satisfies the failure condition), and rejecting the bet closes off the path where I win the bet (can't win a bet you didn't take), so my choices are between losing the bet and not taking the bet. Out of the only two options available to me, losing the bet costs me a dollar, not taking the bet costs me nothing. Quod erat demonstrandum."