Permit me to substitute your question: TDT seems pretty neat philosophically, but can it actually be made to work as computer code?

Answer: Yes. (Sorry for the self-promotion, but I'm proud of myself for writing this up.) The only limiting factor right now is that nobody can program an efficient theorem-prover (or other equivalently powerful general reasoner), but that's not an issue with decision theory per se. (In other words, if we could implement Causal Decision Theory well, then we could implement Timeless Decision Theory well.) But in any case, we can prove theorems about how TDT would do if equipped with a good theorem-prover.