[AZKen]

Don't know how many miles you drive per year but it could take 10 years to recoup the cost vs gas mileage gained. The motor is made to run well on all OE ratios. The rule I go by is: what am I gaining and how much will it cost and what is the risk. Known as: If it ain't broke, don't fix it. I would never pay $700 to have someone mess with all that shimming and etc.
If you really must change ratios, I would buy a good rear end for $150 from an era correct donor (and try to get a posi diff if I could). Easy to install DIY. Then sell my 3.54 diff for $150 to a guy who wants to increase acceleration.

The std rear end for 62 Chevy was 3.90. Options were 3.38 and 4.11. 1T and up had more options. 3.73 and 3.07 came in 1963.(enough about Chevy).

Disclaimer:
I don't know the options for GMC and if there would actually be a 3.07 era donor. A 1963 with 3.07 may fit with no difficulty. Not sure.
Standard 1962 Chevy came with coil rear. Standard 1962 GMC came with leaf rear. You could special order to switch either.
Leaf rear would be super easy DIY swap.