@yer_momma
your math is wrong
You aren't doubling 2k res (comes from the 1920 in the 1920x1080 of 1080p) to get 4k res (comes from the 3840 in 3840x2160 of 2160p) even though it might sound that way because of the 2k and 4k marketting terms, but you need to take into account those terms refer to only one of the two dimensions of a rectangular video format. Both dimensions are doubled so that's 2 dimensions times 2 each, or basically quadruple, not double the amount of pixels on the screen since you can basically fit four 1920x1080 boxes inside one 3840x2160 box. So, at 4 times the res I don't think it will look even close to the image quality of your 1080p projector, which btw cannot produce anywhere close to the quality of a modern 1080p tv.