Not your screen monkey (he/him)
If I wanted to emphasize the "Back to the Dungeon" slogan, I'd play a lot of dungeon crawls.What else would you play up to make a D&D 5e game reference D&D 3.Xe in small ways?
I ran a lot of 3e games based on AD&D adventures that I had converted and I've done both AD&D and 3e adventures I've converted to 5e. And I have yet to find one that didn't really work because of the edition. So I have to say that I don't think there has to be loads of variance between editions whether 1e/2e, 3e, or 5e other than experienced through specific mechanical differences. If you approach your D&D editions based on a personal approach and style that doesn't focus on exploiting the differences between editions, then D&D can feel pretty consistent. For example, we didn't invest heavily in magic item creation or markets when we first started with 3e and so 3e didn't feel quite so different from 2e.