A 6v starter can be used with a 12v system without any problems.. Just don't hold the key for long time if it doesn't start in a few seconds.
Switching to a 12v starter will require a new flywheel since 6v and 12v starters have different gearing.
Have the old starter rebuilt. There are a lot of qualified rebuilders. I'm sure there is an old time auto electric place up there in Detroit that can rebuild your old one.
If not, call Then and Now Automotive.
www.then-now.com