couple of things to keep in mind, the brightness of the image is directly related to the output of the projector and the size of the image, so a home projector might be fine for a smallish image but as the image gets larger it gets marginal (for instance a 1700
lumen projecto is the minimum for a 12 foot image in low ambient light.
a mirror is usually the only
practical way to reduce the distance. If you draw out the triangle that you will need to place the projector at the appropriate distance from the screen to get the image size you need (assuming the brightness is acceptable) you can then fold that triangle using a mirror. To give you a rough Idea, say you need 14 feet from the projector to the screen, but you only have 8 feet of distance, you could then face the projector away from the screen, place a mirror rigidly 3 feet away from the projector angled (remember angle of incident/angle reflection) and this will have the effect of adding 3 plus 3 plus the 8 feet to give you the distance.
Here is a link
Angles of View
You can get mylar film mount it to a piece of plywood with some degree of success, remember the mirror has to be larg enough to fit the image size projected at that distance (in the above example projector 3 feet from the screen)
Sharyn