Tumbling them long enough to really do any polishing may not be a good idea. I do tumble loaded pistol ammo all the time, probably 100,000 rounds have been through my tumbler. I just run it for a couple of minutes to remove the sizing lube from the cases and thats all.
If a couple of minutes is changing the burn rate it does not show up over the chrono.
There is no way on this earth that a loaded round could develop enough speed inside a tumbler full of media to set off a primer, major manufacturers tumble loaded ammo all the time (for a few mins) with no apparent ill effects.
My rifle ammo that may sit for 6 months or so is handled with gloves on from the time it leaves the tumbler until it is in the ammo box, no oil on the cases, so oxidation over time. But I like shiny clean ammo