The LG AU/HU810P has vertical and horizontal lens shift as well as a dual laser light source and puts out approx 2800 lumens.Digital keystone correction sucks. Best to get a PJ with at least vertical lens shift I think @wittaj. projectorcentral has calculators for that sort of thing. I just don't know how accurate they are for all models.
There are lots of projectors roughly the size of a (thick) game console, but I have only seen lens shift on substantially larger models than that.Mine was a beast 20 years ago, so hopefully the newer ones are smaller lol.