Hi Tom,
I had that exact pinion gear failure back in 1964, and it disabled my Coupe for a few years until I could afford to fix it. The pinion in my Coupe broke loose while I was driving at speed on a highway. What a mess it made.
Re stainless steel, it will cause galvanic corrosion of most carbon steels it comes in contact with. So it isn't good to mix stainless with other grades of steel.
As for the various types of stainless / corrosion resistant steels, this site defines the various alloys:
https://continentalsteel.com/stainless-steel/grades/