8.25 carrier wear

That's gonna be your little secret. And it's WRONG. Imagine all the tiny metal particles that made their way into and through those bearings and all the rest of them. If you don't start all over with a BARE housing and clean it operating room clean, you better be prepared to do this all over. Again.

I know it's not the perfect way of doing it, but like I said I'm planning on replacing the whole rear end within the next year or two, so I'm just looking to get it back together and driving.

That's it right there.
If the cross-pinholes are egged out, the crosspin retaining bolt or roll-pin, as the case may be, is gonna come under a lot of pressure. When it fails, the pin is gonna want get the heck outta Dodge,lol. If there is room for it to get by the ring gear, then it is heading for the back cover, where it will probably not make it all the way thru. So stuck there as it is, it will lock up your entire rear end and skid the tires. If this happens at 20/30 mph, you just get a heck of a scare. If it happens at 60, the back end is gonna spin around in a heartbeat, and it will be impossible to steer the car. At 60 mph you are traveling at 88 feet per second, with no steering and the brakes do not do much when careening sideways, so basically you have become an unguided missile.
Pray it doesn't happen in traffic.
It doesn't matter if the pin doesn't make it to the cover, no matter where it stops, the result will be the same.
If you tack-weld it in, the slop where the side gears formerly resided will eventually break the tacks. So if you weld it in, make sure it never comes outta there. Ohhhhhhhhhh, wait........... lol. You better put new wheel bearings and seals in, now, followed by the C-clips and then weld in the cross-pin, cuz you won't get another chance.

That's a good point, I had a 7.25 that lost some teeth on the ring gear and locked everything up. It was on the on ramp so it was fairly low speed. I'm about to check if the local pull a part is open today and if it is go see if I can get a new carrier. I don't have anything else to do in this quarantine lol

As far as getting the housing clean, I still have a case of brake clean.