Yep, this all seems correct; the player does not have enough degrees of freedom to prevent there from being a fixpoint, and it is possible to prove for all interpretations that no strategy does better than tying with the simple one-box strategy. But I feel, very strongly, that allowing this particular kind of ambiguity into decision theory problems is a reliably losing move. That road leads only to confusion, and that particular mistake is responsible for many (possibly most) previous failures to figure out decision theory.