Seven pages of great discussion mainly recommending D&D as the replacement for D&D!You already have 7 pages of great recommendations and discussion, so I'm not sure if you settled on anything yet.
You didn't mention if your prefered GM style is to homebrew your own adventures or if you prefer to run published adventures. One thing I always look at is how well supported is the system? It may have the greatest rules ever written for the style you are looking for, but if you have trouble finding adventures for it, are you okay with that?
In my experience, DCC gave the best fantasy dungeon exploration style of play that still felt different than D&D. I've backed Goodman Games Dying Lands kickstarter. I'm liking what they are doing with magic from what I've seen so far. Their Lankhmar set is also worth looking into.
You've already stated that more old-school, rules light systems were not well received by your players. So I think Swords & Wizardry is probably out. Even lighter systems like ICRPG as well.
If you want to go full home brew, use Cortex Prime to build the system you are looking for. That may be more work than you want, especially since you'd need to homebrew all your adventures as well.
Usually, when I want a break from D&D, I go with something radically different either in terms of genre or system (or both). But you don't seem interested in that.
All and all, my best recommendation would be one of the DCC setting sets, like Lankhmar or Dying Lands. Already DCC has a familiar but different flavor to it. Lankmar and Dying Lands add to that with heavily flavored new mechanics and settings.
The obvious non-D&D alternatives have already been mentioned. DFRPG, TFT - or In the Labyrinth - which suggests its purpose, Dungeons with hexes. Melee is free from SJG.
Runequest. Runequest Classic is probably the best option because early Runequest was very dungeon based. Pavis is the mega-dungeon and Balastor’s Barracks the classic dungeon. The Mythras variant has a Classic Fantasy supplement that optimises it for dungeons. Plenty of modules. Personally, I would opt for the OpenQuest variant; it has the shallowest d100 learning curve. An OpenQuest Dungeon supplement is promised this year.
Other options:
DragonQuest. More d100. Some great Jaquays adventures.
Palladium Fantasy Roleplay. It is 1d20 roll over so D&D adjacent. Great armour system. Parrying and dodging in combat. We enjoyed this one.
Dragons & Demons. Swedish “D&D”; originally d100 roll under; now d20 roll under. A new version is Kickstarting from Free League but there is a Quickstart.
Advanced Fighting Fantasy. 2d6 roll under. Good Quickstart.
OLD is dungeon optimised. Additive dice pools with d6s. Surely A5E is D&D?