One thing to remember is that a 6v starter will work in 12v especially on a car that starts quickly and isn't a daily driver. The pinion gear might also interchange. As said before I think all of these engines (228-302) came with big flywheels (4 & 6 bolt patterns) the change was a difference in teeth between 6 & 12 volt. You could change the ring gear on the flywheel. You could on a stock flywheel not sure about yours. The flywheel themselves are the same size.
I remember when I first put the 270 in my '53 pickup it was still 6v. The engine was from a 12v '57 pickup. It would start when gold. Warm it would start when pushed or rolled down a hill.

A six volt starter would not mesh. Maybe that is what you are running into. I have some old parts books maybe I can find a part number for you. It won't happen today.
Is this it?
Starter Drive Link