Zach, I don’t know if this will help you or not, but years ago I bought a nice tiffen 62mm circular polarizing filter for another camera outfit. When I bought my canon gear, I bought a 62 to 58mm adapter ring so I could continue to use the polarizer with the 58mm Canon lenses. I’ve not had any vignetting issues with it on any of the lenses at the widest angles.
You might think about an 82mm polarizer with an adapter ring. ???
Zach I have the Nikon Filter on a Sony R1 – basically same chip/factor as you have I believe- with no vignetting at 24mm, my widest.Very nice filter and well worth the money IMHO. It’s very slim by comparison to other polarizers I have had and seen. I suspect the larger filter/adapter ring may be your only option at 12mm.