I have a question that is probably stupid and/or already discussed in the comments. But I don't have time to read all the comments, so, if someone nonetheless would kindly explain why I'm confused, I would be grateful.

The OP writes

So E does indeed "depend on" C, in the particular sense you've specified. Thus, if I happen to have a strong enough preference that E output True, then TDT (as currently formulated) will tell me to two-box for the sake of that goal. But that's the wrong decision, of course. In reality, I have no choice about the specified digit of pi.

It seems to me that TDT should just bite the bullet here. By hypothesis, I really want E to output True. Let's say that E represents the output True by flashing a green light.. Note, the issue isn't that I want the i-th digit of π to be 0. Rather, I'm just really really keen on seeing that flashing green light.

So I pick both boxes to maximize my chance of seeing the green light flash. After all, if the light flashes, I leave the game overflowing with utility. But if I'd picked only one box, I would be guaranteeing that the light doesn't flash. Why would I want to do that?

ETA: Gary Drescher gives an explanation here for why two-boxing is wrong. But I don't understand his explanation.