I have been experimenting with the use of Thompson Center Natural Lube 1000 to protect the bores of some of my shotguns.
I have been using this product as a patch and bullet lube, and as a bore protectant in my flintlocks with excellent results. Before using this, no matter how much I cleaned, and scrubbed, and boiled, and dried, and oiled, I still got some after-rusting in the bores during storage. Since I made the switch over a dozen years ago, I have had zero problems. I reasoned that if it did that well with black powder, it might do at least as well with smokeless. It has not disappointed me. It is a non-petroleum product that has the consistancy of grease, so it is unlikely to run off as gun oil will over time. If you warm the barrels slightly, it will readily melt and get into the bottom of any pits that may be there, and thus keep them from getting any worse.
