What if you rotate the camera slightly while you move? By the time you reach the end of the physical room, the camera is facing the opposite direction in virtual room and you have to turn around.
http://www.wired.com/2015/08/cant-walk-straight-lineand-that...
For the other idea, the game could pause during rotations. Would be annoying, but it wouldn't destroy the game mechanics.
No solution is going to be perfect. I think people interested in this will probably have to do it outdoors, or at some public space.