(Vague, speculative thinking): Is the time element of UDT actually a distraction? Consider the following: agents A and B are in a situation where they'd benefit from cooperation. Unfortunately, the situation is complicated—it's not like a prisoner's dilemma, where there's a clear "cooperate" and a clear "defect" option. Instead they need to take long sequences of actions, and they each have many opportunities to subtly gain an advantage at the other's expense.

Therefore instead of agreements formulated as "if you do X I'll do Y", it'd be far more beneficial for them to make agreements of the form "if you follow the advice of person Z then I will too". Here person Z needs to be someone that both A and B trust to be highly moral, neutral, competent, etc. Even if there's some method of defecting that neither of them considered in advance, at the point in time when it arises Z will advise against doing it. (They don't need to actually have access to Z, they can just model what Z will say.)

If A and B don't have much communication bandwidth between them (e.g. they're trying to do acausal coordination) then they will need to choose a Z that's a clear Schelling point, even if that Z is suboptimal in other ways.

UDT can be seen as the special case where A and B choose Z as follows: "keep forgetting information until you don't know if you're A or B". If A and B are different branches of the same agent, then the easiest way to do this is just to let Z be their last common ancestor. (Coalitional agency can be seen as an implementation of this.) If they're not, then they'll also need to coordinate on a way to make sure they'll forget roughly the same things.

But there are many other ways of picking Schelling Zs. For example, if A and B follow the same religion, then the central figure in that religion (Jesus, Buddha, Mohammad, etc) is a clear Schelling point.

EDIT: Z need not be one person, it could be a group of people. E.g. in the UDT case, if there are several different orders in which A and B could potentially forget information, then they could just do all of them and then follow the aggregated advice of the resulting council. Similarly, even if A and B aren't of the same religion, they could agree to follow whatever compromise their respective religions' central figures would have come to.

EDIT 2: UDT is usually prone to commitment races because it thinks of each agent in a conflict as separately making commitments earlier in logical time. But focusing on symmetric commitments gets rid of this problem.