Do you already own the projector? If so, what kind? Where are you planning on running the video source from?
If all you are going to use it for is movies,
etc, then I would recommend using rear projection. Do you have clear access to the rear wall? Would there be enough room to mount it on a shelf there and still have clearance for your
cyc? If not, I recommend scaffolding, not a cart. Flying projection in a theater is a possibility if you have the right set-up, but as you theorized, you will likely have some drift in your image and focussing your image can be a real pain in the behind. With rear screen, you want your projector to be as centered on the screen as possible (a luxury that you rarely have with front screen), which is why you will want the height offered by the scaffolding.
If you are forced to put it
FOH, the scaffolding can again offer you flexibility. Draping scaffolding is common practice and a great use for old soft goods. If the large drape that splits your
auditorium has an opening in the middle, theoretically you could use that to hide your setup.
Obviously you will need assistance with either temporary setup. Two people can accopmlish this task (I have done it quite often).
Davin