What Muley said! I'm loathe to clean up brass that is containing live bullets and powder that I expect to use for serious business in future, but it can be done judiciously. I'm guessing you will likely never fire those original rounds anyway, right? I would suggest some Never Dull Magic Wadding Polish for all kinds of metal. Its a soft stuff that won't scratch unless dirty with grit. It's a yellowish wadding contained in a round can about four inches in diameter and about the same height. Measurements are my estimates! Pinch off a large enough piece of the wadding and polish each cassing with it. Doesn't take long, but it takes a minnit or so, and does not leave much if any liquid on the metal. Let it dry for about a couple minnits and then polish the metal with a clean dry soft cloth. Stuff works great on bullets and silver stuff too! A can will last you forever, and unless you just flat wear out the small wad you use, you can put it back in the can and reuse it till it's black and worn out. I see it in the cleaning product sections at grocery stores, etc, and I'd bet a hundred dollars you can find it on Amazon! Doesn't cost much either. Of course, my can that's years old is still half full of the stuff. I do think it may have dried out a bit in time, but it still works OK. Clean up that ammo and store it in a regular divided cartride box. You can also clean the green stuff (verdigris) off the leather too (NOT with the Never Dull!) and that old rig will be standing tall for the future. I say again, what a treasure!
BTW, that never dull will put a shine on that brass Sam Browne buckle and other brass parts on the rig! It may have to be repeated in time, but just wipe off your fingerprints when polishing and refrain from touching the brass with your fingers and the shine will last a long time!