I’ll give you the advice that I’m slowly taking myself: commit to running a full D&D 5e game to 20th level. The game gives you a framework for measuring progress (“We’re halfway to 20th level.”) and clearly defined end goal (“We’ll stop at 20th level.”). If things start to drag, maybe boost the experience point figures a little, but stay committed.
The “heavy lifting” you’re worried about is a feature, not a bug. Get away from the indie game commandment to play the RAW. Use 5e as a chassis to create a homebrew D&D game that fits your group like a tailored suit. Plunder those trad books you love for d20 rules to bolt onto 5e’s framework.
At it’s core, 5e is a very rudimentary system. You’ll need to create interesting rules to liven up fights and other encounters. This will hopefully scratch your critical, game-designer side.
Don’t think of homebrewing as creating legal precedent or hacking solutions out on the fly. Every RPG involves making judgment calls for edge cases. That’s not onerous. It’s part of tabletop RPGs. Hell, you can change your mind later on a ruling if you want. Stick to the rules, but be relaxed about it.
From what I gather, you’ve got a great group of players. They can make every game fun. They’ll make D&D fun. Ask them to commit to 20th level. Entice them with promises of vorpal swords and wish spells.