JACOB,
As Tiny indicated, testing the 6 volt motor on 12 volts certainly wouldn't be instant death for it, and it appears he has run his on 12 volts for years.
If it works on 6 volts, leave it alone. The Grainger 12 volt is not a
direct swap for the stock unit.
Using a replacement 12 volt motor on your factory 6 volt system might give you a 'slow motion' motor (Tiny)...which could result in frozen mammaries!
Stuart