Well they don't rub. I have a few more fender wrinkles to dolly out and that should help. I also think the tire pressure is a little high. Might go to 10" rims.
Or like you say I'll slide a few sheet metal washers in there.
Because you are using the same ring gear/ pinion combination in the same case the pinion shims shouldn't need to be changed. I would remove the ring gear from the carrier and set the preload, then reinstall the ring gear and shift the shims from one side to the other to get backlash set. Removing the ring gear will allow you to turn the dif without having to remove the pinion.
On a side note, they used rivets one, because they are cheaper than nuts and bolts and two, the rivets swell in the hole to completely fill it and don't allow the potential for any movement which can cause eventual breakage.