But if a rational agent disprefers ambiguity, then it rejects bets (1) and (2) in the coin toss game, but accepts their agglomeration. And if this is so, then there is no credence it can assign to H that to make its actions consistent, so how could it possibly be a Bayesian?

Sure there is. To someone with ambiguity aversion, "heads in situation A" and "heads in situation B" are different things. They wouldn't be indistinguishable H's and assigning a credence to one doesn't imply assigning the same credence to the other just because they both have heads in them.

(I'm not sure that "credence" is really the right word for what you are describing, either.)