That's a nice gun. I keep saying, thinking that some day I'll get one, or something like it, and sleeve the left barrel down to a rifle, and have a really cool combo-gun. However, my other rifles and muskets may never get used again, so I refrain.
I think the best solution to the empty space at the breech end would be to clean and dry the cavities very well, stand the barrels perfectly vertical on the muzzles, and pour in/fill up the cavities with a good bow-makers epoxy or JB weld. JB weld does not flow great, but if the breech was nice and warm is should settle good.
Having said that, your cleaning method, and using carb cleaner and WD40 should prevent any rust from forming.
On leaving barrels in the white, I did this with both my Brown Bess, 1861, and Jeager. Getting that gun-metal grey is very nice, but it takes a lot of time and patience. Takes a couple years at least, but worth it. Some barrels rust more easily than others. My Jeager's Colerain barrel does not seem to rust at all. I hunted off and on drizzling rain with it just recently...no rust, not even a tiny spot. It's like it's stainless or something...but it is turning slowly but surely. The Bess, just barely. I've never seen a spot of rust on my 1861 Springfield, and she's been out in heavy rain, but it has turned the nicest grey.
I have two Miroku rifles that will rust if you even sneeze within twenty feet of them.
With all three guns I avoid getting any oil on the barrels, (when cleaning I might wipe it down lightly with a dirty rag) and wipe my sweaty hands on them, and generally put my hands, preferably dirty, on them often, and rub them down with dirty or sweaty hands. !!!! It also seems to help, if when you clean the gun, and take out that first dirty, black, gooey patch, to rub the barrel down with it.
I try not to let them actually rust, and if I see that happening I will wipe them down with some oily solvent, gently, sparingly, then wipe dry.
