RedGreen - thanks for the link. What they call "flip" is really a 180 degree clockwise rotation rather than a flip, so it doesn't solve the problem in my case.
Dinwiddie - since I'm planning to use this with live video, it really doesn't help to use video editing software. I'm looking for a solution - probably a driver-level solution as you say - that will do the inversion in real time. It is exactly what you say: a 180 degree rotation followed by left-right mirror image, or else a vertical mirror image with no rotation. Both have the same end result: top goes to bottom, bottom goes to top, but left and right are un-changed. Left stays left and right stays right.