Since there was obviously a leak at the flange in the past, there is great possibility that nasty water got under the tile, into the backerboard. If the cast iron isn't the source of the stank, then consider pulling up tile.
Barkeeper's friend is also a mild acid - oxalic acid. I use it on my stainless steel pots and pans. The can also suggests its use on porcelain toilets. As well, it suggests its use to remove rust stains from concrete driveways. I can tell you that it does wonders removing burned-on stuff...
Glacier Bay....check the cartridge and seals. I'm guessing a low-flow showerhead is causing the shower's hot water to feed over to the cold line, of vise versa, and the increased pressure in that line is backing up to the point of least resistance, being the crappy Glacier Bay faucet.