I think in 62, they were still cast iron...maybe it was mid 62 or 63 when they changed to the aluminum ones.....If it is aluminum, any Chevy aluminum short tailshaft powerglide should fit it. Quite common up through early 70s
Personally, I would look into adapting a T350 or even an overdrive tranny......same bellhousing.
If that was my car I would't hesitate putting in a 200R4 as they are the same length the only thing to change is the driveshaft yoke as yours should be course spline with a later model turbo 350 or lots of others that have the fine spline.The only other thing is the crossmember as the trans mount is a little farther back,so keep the original trans and crossmember so it could be changed back with no problem and make a new crossmember. You will also need to make a bracket for the kick down cable which is VERY important. Any good trans shop can do this for you.