you did well, especially if you like the gun as is. Don't know the answer to your frame question but I'll look at my old Savage catalogs and see what I can see. I SUSPECT that the 16 and 12 were made on the same frame, since I've handled both, but I've never handled a 20. One of my old hunting buddies from NYS has a 430 16 guage his dad gave him about 50 years ago (it was used THEN) and is deadly on grouse with it. 26" IC/M.
16 guage shells are still very available, even here in CA, just not in the variety of loads that other guages offer. Enjoy your old Savage!