I say take advantage of both your burned-out state, and the rules-heavy desires of your players:
Run nothing but pre-packaged modules, with the barest, flimsiest of plots. Spend just enough energy to come up with a couple of exotic locales to run combats in, with the occasional new rule to make things challenging. Make it so over the top high action that even the players can't believe it.
In other words, turn D&D into a Feng Shui Session.
Eventually, they will want something with more substance, and so will you.
Whatever your solution, good luck in it. It may be as simple as just giving up and vegetating a while.
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I've been missing something from my game sessions, too, lately, though I'm not sure what to do about it:
-Until a year ago, my group and I used to game from say 3pm until 11pm or midnight. We'd game until 6:30 or 7, then we'd break for dinner, eat at an inexpensive restaurant, and "shoot the bull" for an hour or so. We'd go back to gaming, game until 11 pmm or midnight, and break for home. Then, at several players' request, we rolled it to 12 noon to 6pm, and then break for the day. In some ways, I miss those bull sessions, because we got to know each other in more than just our esoteric game knowledge; we'd discuss politics, religion, philosophy, current events, etc.
Our schedules only permit us time to get together once a week, and we don't want to miss our gaming time, which is still going strong, but in some ways I miss that B.S. time in between the gaming.
Heck, at the ENworld Gamedays, the dinners are half the fun, for the same reason - you're more than a screenname and a character.