Projector advice? (cheap, gaming, shelf-able)

[rainbowbattlekid]

So I had been looking at the Epson 2040 and it seems to be a good price, cheap replacement bulb, and good low input lag.

However, the main issue with it is: the lack of lens shift and the short throw distance give me very limited options on where to put it, and we have a small apartment so it would most likely be in the way(unless i could find a mount that easily swivels it up 90 to the ceiling and back).

If I can get around having to mount it, and can just put in on top of a shelf in the opposite corner as the screen, that would be ideal.

So is there an LCD projector(rainbow effect bugs me) that is 1)AROUND $1000 or less, 2)that I can put on a shelf about 13-16' away from a 106" screen, and 3)has input lag comparable to the Epson 2040?

Thanks for any recommendations!