I'm trying to think now how you'd represent the whole action economy of 4e in a system which usually has a very different action economy, as well as all of the other things that are very different in a traditional roguelike. Minor brainstorm incoming:
First of all, representing the Standard/Move/Minor durations. I'm thinking something like attacking being 10 time (choosing a number large enough to give me space while still using integers), minor actions being less than 10 time (depending on how minor the action is... could have this be 5 or 2 to start with and see how things go from there), and move actions being an amount of time depending on your movement speed (probably low... 5, perhaps? 4 for fast races, 6 for dwarves). Not sure how you'd represent shifting at all, given that part of what makes roguelikes so interesting is that positioning is everything. Maybe a 10 time movement that doesn't cause OAs.
And that's another thing that changes things. In a roguelike, you can retreat from a monster with equal speed, and it will follow you across the map. So what if instead, moving while next to a monster is slower, instead of there being special oppourtunity actions. (I realise that I have seen this idea before, in the remake of Avernum, but it's quite effective.) Immediate actions would need some similar rethinking.
The next thing to think about is AEDU. Now, obviously, At-Wills aren't an issue, and Utility powers can be treated as their usage limit. Encounter powers are only recharged by, essentially, not being used for a while. So you could just put a large recharge timer on them (500 time feels like a good starting point). Or alternatively, have a "short rest" command that waits for a length of time, and if there are no interruptions, Encounter powers are regained. I think I prefer this option less, though, as the whole "forced rest" thing makes roguelikes boring, and is already an issue for 4e.
Which leaves Daily powers. Now, an extended rest is something that's close to impossible to take in a dungeon, so a really long wait is out of the question. There's the obvious point that leveling up gives you the effects of an extended rest, which makes for some very interesting risk/reward decisions as you're close to a level, but how about also designing the dungeon around the floors being just enough that, afterwards, you need an extended rest, and then giving the player an extended rest between floors. Obviously, this would only work for a roguelike where you can't go back up again (or at least, can't easily go back up again). And you could make "diving for safety" a lot harder by having some sort of quest to unlock the doors down...
I'd think about this some more, but right now, it's 8am, and I haven't gone to bed yet (oops). Hopefully I've left you some things to think about...