One thing we have not checked out yet: Are the cases showing any signs of high pressures? Things like cratered primers, pierced or leaking primers, a little button of brass extruded into the ejector plunger hole, and so on? These are indications that you do have high pressures, which will extract hard and cause ripped rims. A civilian throat with military ammo can cause this... So you can shoot suitable ammo or have a military reamer put into it, which seems a shame for a good barrel like this has.
The concerns about getting abrasives into the throat are valid with some polishing agents, but not others. I feel that polishing is important in autoloading rifles, while some other folks think that it is unnecessary...
I know some folks who use Flitz on a mop. Flitz is probably OK. If you get some on the throat, just patch it out. JB won't hurt barrels and I doubt it will polish the chamber much, but some folks swear by it.
I use a tapered wooden dowel with slit in it and use 220 wet-or-dry. Polishing this way should be on the body only. You can get onto the shoulder, but it won't do any good up there, and trying to do the neck is an invitation to messing up the throat, so just do the body.
Remember that all you are trying to do is take off the meat hooks (high spots, asperities), not change size or make the chamber bright. It is always easier to do this with the barrel off of the upper, but it will work with it installed too.
Try some commercial ammo, and maybe polish the chamber, and try the rifle out. If you have no high pressure indications, the chamber is polished, and you still rip rims off, do not despair, just get back with us and we can go from their.