I think newcomes problem can be resolved by throwing out the idea that a decision is being made at any point. We're mixing levels or engaging in a kind of category error where the there is a chain of three deterministic events that lead to an outcome rather than a decision point that can go either way. The nature of the person receiving the box is analyzed, that determines the contents of the box, and then subsequently one or two boxes are taken as a consequence of determined nature of the Box taker not a free choice or even the contents of the boxes. There is no decision.

The essential problem is that people try to conceptualize this problem both in terms of limited knowledge subjective decision making which generates the illusion of choice and erroneously try to reconcile that with an objectively deterministic universe, Heisenberg uncertainty notwithstanding.

An additional point of subjective confusion comes from the fact that knowledge of the nature of the problem affects the state of the box taker and may change whether one or two boxes are taken. That creates the subjective experience of a decision but objectively it's simply another factor contributing to the cause effect chain.