"snorkel lenses" look ridiculous on large projectors.
https://epson.com/Accessories/Projector-Accessories/ELPLX02-Ultra-Short-throw-Lens/p/V12H004X02

Goes in the front like a normal lens, shoots backwards like a cursed lens.

The problem with short-throw lenses is that they will exacerbate any geometry issues. So aligning them is hard. And ANY tiny little non-planer issue with the screen surface gets massively multiplied.
You can get away with a lot of issues using long lenses. Short lenses are a pain.

ETA:
Linked is a 0.35 ratio lense.
So for every 0.35m from the screen, it will project a 1m wide screen.
0.7m away? 2m screen. 1.25m away? 5m wide screen.
3.5m away? 10m wide screen.