The per diem paradigm is broken. It ruins pacing, creates perverse incentives, and forces a specific encounter schedule on the GM.
Until you somehow house rule all per diem abilities into continuously recharging or per encounter/scene abilities you'll have a problem.
If you can't fix the problem you should use no dungeon longer than the party should be able to get through. That's 4*APL total CR per dungeon for parties built like the iconics and probably not more than twice that for any but the most heavily optimized and efficiently played parties.
Or you can let them rest with impunity, or just ignore the concept of sleep and recharge everything every X*APL CR of encounters. It's ugly and metagamey but something like this is necessary.
CR is per encounter. It can't not be per encounter. That means to have a balanced game everything has to be per encounter. Per hour can be made to sort of work if you really despise per encounter mechanics, but only in as much as they approximate per encounter mechanics.