Bryan,
The 1912 stock may work and it may not? Fox changed the radius where the tangs meet the stock head over the years. If these Radius don't match they cannot be fit. Even if they have the same radius it still may be a real problem to fit a stock from one gun to another. Foxes were not the precision machine made guns we have today. There can be dimensional differences in them from gun to gun and era to era. You are correct that the 16 & 20ga were based on the same frame size, but with that said it doesn't mean they will interchange stocks.
I suggest you visit the Fox collectors site and post your question over there and possibly add some pictures of both your gun and the stock your interested in buying. It may be more cost effective having a new stock made or yours repaired.
http://www.foxcollectors.com/
