The more I have thought about it, the more I like the idea of weldingin a 3/8" I/D sleeve once you have drilled out the hole. This will help in 2 ways:

I know once I have the top hole line up, the slop between the pin and the hole can cause the pin to shift at an angle and make it tough to manuever the pin down through the bottom hole. With a sleeve it should help eleviate this...although you still have to match up the lower hole.

It would also help in allowing the hinge to be snugged down, either through a clevis pin or other method without distorting the hinge "ears"