The projector is irrelevant unless you can rule out all ambient light - and you can't because the screen/projector themselves will contribute to it. This is an inherent problem because the screen needs to be reflective otherwise it won't show your projected image but if it is reflective then the base black level will also be far from zero. Emissive displays don't have this problem because you can increase the emissive brightness without raising the black level and even LCD screens do better because you can increase the ratio between the two with better LCD tech.
> This is an inherent problem because the screen needs to be reflective otherwise it won't show your projected image but if it is reflective then the base black level will also be far from zero.
Screens (ALR) for these projectors only reflect from a single direction (down) and are less reflection than a standard TV screen (which are generally gloss screens) from other directions. That is, both in personal experience and in reviews, they are generally considered equal to high quality LCDs in contrast and in color.
Their main detraction from using as a display is that they are big and are generally paired with large (>100") screens.