After putting the axles back in with seals and it bolted together, I ripped it all apart again. Got as far as taking the carrier out.
I hope you checked the backlash before screwing with the shims 'n' adjuster nut. When it goes together, it's going to want to be at the SAME backlash while also having proper bearing preload.
If you're going to put a heap of miles on this thing, sure, a new ring 'n' pinion is a good idea.
Setting pinion depth is the hard part. Getting backlash right isn't so bad. If you're not replacing the ring 'n' pinion gears, for ****'s sake do not screw with the pinion.
If this isn't going to be a high-mileage vehicle,
I'd have thrown two extra magnets into the housing and looked-in on it after five thousand miles. (Or earlier, if it's actually noisy.) From a certain perspective, the ring gear is already ruined; and the pinion is matched to it. As long as you don't screw-up any of the other bits 'n' pieces, you've got little to lose by putting it together and seeing what happens.