Going from 5/16" to 3/8" would probably not be practical. There wouldn't be enough wall thickness to bore it out and re-tap it without danger of the insert turning into a loose brass spring. I would avoid the change if possible but if it was necessary to change the size I'd probably remove the old insert, plug the shaft with phenolic and bore and tap the phenolic to accomodate the larger pin.
just more hot air!
Sherm