Was there some expectation as to how often long rests were possible? Put another way, could you still have balanced fights if you only had one per day? I'm trying to understand what the norm was (if there was one). I know that your'e supposed to have several combats between rests in 5th (though most people don't), and I'm wondering how 4th handled the '5 minute adventuring day' problem, if it was a problem at all.
Thinking more about my experiments with 4e, that you may find useful:
Milestones (briefly mentioned above) were a "lever" that tried to encourage parties to continue adventuring. A milestone was met every 2 encounters. You gained an action point, and initially, an extra use of a magic item daily (which started at # per Tier, like 1 use at Heroic, etc.). Daily magic item usage was changed by Essentials IIRC. Action Points gave you an additional Standard Action that encounter. But Milestones reset if you took an extended/long rest. Hence, the incentive to carry on.
One of the things I tried was requiring the use of an Action Point to use Dailies/Signature Powers (so not limited to only once/day). I made them more plentiful by awarding one per encounter and counted Skill Challenges/Battle Challenges as encounters. It worked pretty well but ended up with the system I had described above.
I'd encourage you to play around with the 4e "widgets" of Healing Surges, Dailies, Action Points and Milestones [1]. My players and I had a lot of fun experimenting to see what worked best for us, and in fact, our preferences evolved over time.
EDIT: [1] Like, should Dailies be refreshed based on time (short rest, long rest) or a fictional unit (knowing Milestones are fictional units)? How many Dailies should be spent per encounter? Should that be encouraged or discouraged? B/c combat can be long, we tended to encourage use of Dailies (usually 1-2 per encounter), but all-out novas were rare.
Should healing surges refresh the same way as Dailies? For a long time, we had healing surges refresh after short/long rests while Dailies refreshed on Milestones and eventually other fictional units (Story Points).
Let us know what you come up with!