Speaking from a collectors point of view, many people generally prefer a piece left as found, and nothing done to an item that can't be undone or reversed. Removing and stabilizing rust (especially the red stuff) is fine. Re-conversion of pieces that were once flint, turned into percussion pieces, and then made into flinters again can raise questions about what else was done and how much is truly original or the result of a highly skilled forger---or restorer. In some cases, "restoration" can badly devalue the piece.
I collect, I also shoot some of them although there are a few that could be fired, that I won't. One of them is a completely original and all intact 1795 Springfield flinter made in 1799. It's too rare to risk damaging, running the risk one of the original springs might snap, let alone one of the barrel weld seams opening. When a piece is old and valuable, it might be best to leave well enough alone by doing the least amount of harm possible.
I would suggest removing active rust and stabilizing the newly exposed metal with a very light coat of fine soft furniture wax. try to avoid oil as the wood can soak it up, and dirt/dust will stick and can build up over time. Wax is easily removed, and on a warm day in the sun, rubs off easily with a soft clean cotton or flannel cloth.
I don't recall anyone suggesting inspecting the bore by using a digital inspection scope that can be inserted down the barrel. These can be bought on ebay and elsewhere. Entry level ones can be bought for about $15 (give or take). There are models that work with laptops, tablets, and cell phones (Windows/Macs/Androids and even linux models!) Using an endoscope will allow you to see the face of the breech and other details, and you might not even want to have the breech plug removed. Something to think about?