I just finished most of the engine I mentioned:
It took me a while, mostly because I took a lot of dead ends. It’s a step beyond the old-school dungeon crawlers you mentioned, but a leap behind what @d954mas pulled off. There are some small graphical glitches (such as the wall texture being deformed on the sides) and pecularities (each texture has to be its own atlas), but overall I’m happy with how it turned out.
From what I learned, the way to go is probably to either make it much simpler like the old dungeon games (if you can’t ever see side walls that are not a part of the corridor you’re in, you can get away with a pre-skewed texture) or just use perspective camera and an actual 3d world. What I did is a weird hybrid that’s not really great, but good enough for my purposes.