Just to wrap up this thread: The item I said I "REALLY" need in post 3 exists. I bought a bunch of 315 MHz remotes and corresponding receivers from Adafruit. The web page says any unit will work with any other, even stating "There is no sub-addressing."
I would have beeen concerned that other people may have the same unit, and unlock my doors. But it's not actually true that they don't have addressing.
All fob and receiver can be addressed with solder bridges, (which must match on all fobs and receivers) with 6,561 combinations.
So... Whether this project is feasible or not doesn't matter, because this is a better solution.