I realized today that UDT doesn't really need the assumption that other players use UDT. In any game where all players have the same utility function, "everyone using UDT" is a Nash equilibrium that gives everyone their highest possible expected utility. So you can just use it unilaterally.
That covers such cases as Absent-Minded Driver, Psy-Kosh's problem, Wei's coordination problem. Notably it doesn't cover the Prisoner's Dilemma, because the players assign different utilities to the same outcome.
(Also this shows how Von Neumann-Morgenstern expected utility maximization is basically a restriction of UDT to single player games with perfect recall. For imperfect recall (AMD) or multiple players (Psy-Kosh) you need the full version.)
You can actually push game theory a bit further, and allow games where players have different utility functions, as long as some subset of players can jointly enforce their highest possible expected utilities. UDT doesn't support that kind of decision-making, but really it should be a no-brainer too...?