So I saw somewhere that someone attempted a low-unlock run a while ago. If I remember correctly, it was unfinished and unlocked some things that weren't strictly necessary, but I liked the idea so I decided to do a bit of a different type of self-imposed challenge to what people normally tend to do in this game.
I give you, the EXTREME no-unlock run:

So, I cleared the entire game with only the following unlocks:
- Lv. 2 of each of the class buildings
- Lv. 0 Bezar (bought the Gate Scroll but didn't upgrade Bezar, got Bargain items and nothing else - this isn't necessary but I figured it wasn't worth restarting to get rid of)
...plus the few subdungeon items I could scrounge up for my 3 locker spaces.
This means every run needed to be Faithless, mostly-Miser, Human-only, and mostly-Purist (the only really useful preps I got were from Mage Tower, which I made sure to upgrade last and only use sparingly). In addition, whenever it wasn't necessary (i.e. any dungeon whose completion requirement didn't include a non-fighter), I went with Human Fighter for maximum simplicity. I also didn't get any of the advanced glyphs or bosses, and I needed to beat Cursed Oasis and Berserker Camp to unlock Gaan-Telet.
This was pretty tough! I'm not quite as pro as some people here, but it made me really use my glyphs in a way I wasn't used to - especially glyphs I usually ignore like BYSSEPS or WEYTWUT. Bargain items were interesting, too. I was surprised that I was able to take out Gaan-Telet in only 2 tries, really - I was worried Human Fighter with no gods, preps, or decent items would be nigh-impossible, but I was lucky enough to get early WONAFYT and Bargain Heart.

This was the only dungeon I couldn't beat as Human Fighter. Shades, Armors, and Thralls only made this Cursed Oasis run very... interesting. It's practically impossible to fight anything higher-level than you as Fighter past level 5 or so, and blackspace is suuuper limited. I decided to go a bit outside of the norm here and prepped Pepper as Priest, mainly cause it's such a funny strategy and I never get to use it normally. Magma Mines and Labyrinth were also tricky, but Human Fighter was able to take them both out with minimal struggling.

After that finished, I decided to do all the other non-Vicious quests under similar rules. I did get Elf to do Unlikely Heroes and Bezar level 1 to unlock the Bank (plus all the level 3 class buildings, obviously), but these were all still Faithless and with a low-level item selection. This run was the hardest, I think - I hate Shifting Passages when you don't have ENDISWAL. Now everything that isn't Vicious is done except Berserker Labyrinth (tried it, don't think it's possible without at least one god) and the later Unlikely Heroes quests (which just seem boring).
So there you have it! I really enjoyed this sort of large-scale self imposed challenge, and I'm sure someone better at the game than I am could take it to Vicious. If anyone has any other ideas for full-game challenges with this one, I'd like to try them!