Really, I think the best solution is to ditch the correlation between character powers and game-world time. Instead, treat "per day" abilities as "per session" instead. Absent very short or very long sessions, it works great--no 15 minute adventuring days because there's not as much benefit to resting. Games that feature lots of weaker encounters can just use a few "per session" resources each fight, while games that feature just a few, more challenging encounters will see the players bring their A game to every fight.
Oh, there are problems with per-session resources too. In a long-time Shadowrun campaign (Edition 1, 2, 3) I was playing in, one very important survival resource ("Karma Pool") renewed between session. I noticed how a very, well, "character-possessive" and dominant player started filibustering when she was low on that pool, and it was apparent that the DM wanted to run just one more encounter before the session was over. Suddenly everything needed to be questioned, clarified, discussed, etc...