I think the conflict dissolves if you actually try to use your anticipation to do something useful.

Example. Suppose you can either push button A (before 11AM) so that if you're still in the room you get a small happiness reward, or you can push button B so if you're transported to paradise you get a happiness reward. If you value happiness in all your copies equally, you should push button B, which means that you "anticipate" being transported to paradise.

This gets a little weird with the clones and to what extent you should care about them, but there's an analogous situation where I think the anthropic measure solution is clearly more intuitive: death. Suppose the many worlds interpretation is true and you set up a situation so that you die in 99% of worlds. Then should you "anticipate" death, or anticipate surviving? Anticipating death seems like the right thing. A hedonist should not be willing to sacrifice 1 unit of pleasure before quantum suicide in order to gain 10 units on the off chance that they survive.

So I think that one's anticipation of the future should not be a probability distribution over sensory input sequences (which sums to 1), but rather a finite non-negative distribution (which sums to a non-negative real number).