So my main question is not for the game, it is a philosophical question on how I should define my epistemic rationality. However, there is also a game I am designing. I don't know what the overall structure will be in my game, but it actually doesn't matter what your score is or what the win condition is. As long as there are isolated questions and it is always better to win that round than to lose that round, and each round is done with the spinners I described, then the optimal strategy will always be honest reporting of probabilities.

In fact, you could take any trivia game which asks only multiple choice questions, and which you always want to get the answer right, and replace it with my spinner mechanism, and it will work.