I found a mirror at home (yay!), that although it has curved edges, the rectangular area that can come out of it is 17.5x21 inches which is good enough for what we need (explanation to come).
Casey and I made some measurements to figure out what the base needed to look like. We wanted the table to be about 40-44 inches high so that you would be able to stand next to it and be comfortable touching all spots on the screen. So we did a test; we measured out 40 inches away from our projector screen and held up the mirror, simulating the distance from the plexiglass screen and the...mirror. Then we moved the projector back enough so that the image would project to the right dimensions. It turned out that the projector only needed to be moved back to right underneath the screen to get to 24 inches high - an equal proportion. So the projected image onto the mirror would only need to be half the size of the desired image - 12x24. But, I should have thought about this earlier, the projector projects out at a 3:5 ratio, and our screen is 1:2, so the projection will be something more like 24x40 instead of 24x48. But, this is okay and we won't miss the extra 4 inches on both sides (which some will be covered up by the frame anyways).
So, we then had ample measurements to make the base and projector mount.
Blog on base construction coming soon!
woot.