How about this 3.6" Lcd?

Find out: This is DIY!

Looks like it will cost you about $99 to find out. Maybe you could check it out with a strong magnifier in the store, to see if you can estimate the LCD resolution. (A big blocky low res image is no fun to watch!)

If the resolution is high enough for you then the next step is to buy it, then carefully take it apart to see if you can get any printed circuit boards and backlight layers out of the way for projection. If you need to extend some FFC cables, that may be possible with parts from Digikey or Mouser that cost a few dollars. (See FFC in their indexes.)

If you do this, please let us know the results. The video input feature would make this very useful for DIY projectors.