Are you free to move the mounting position? If so, arvald has narrowed down the "short throw" range for you. Move the mount waaaaaay forward so that there is minimal interference from the room, and then tweak the dickens out of the keystone adjustment.
If cabling is a problem, you might need to budget a video-over-ethernet extender as well.
Abacus Model 2.5 | Quad-Row FX with 256 Cherry Red Slider Beads | Applewood Frame | Water Cooling by Brita Filtration