Not a criticism of your set up in any way, what gets good results is what matters,, Your work certainly speaks for itself.
But just using the short aluminum rod pinned onto the breech bolster to handle the bbl w/o touching the surface and then stand the bbl on it's muzzle face would seem to be a much easier method.
Then apply the soln to the flats with the bbl held verticle. Up and back down and back up motion covers the surfaces quickly.
The muzzle is left in the white so standing the end on a stool or chair seat makes the application easy.
Then hang the bbl out of the way somewhere with a coat hanger wire hook through the tang hole.
I do just that but w/o the aluminum handle. I hold onto the bbl with my fingers gripping the sides of the bolster.
I give everything a coat of soln but not as picky about the under side flats. They always seem to come out just as well anyway.
Those sides of the bolster get a little extra swipe of soln once the bbl is hanging from the hook and they rust as well.
Simple and no xtra equipment needed.
If you have a ceiling hook, the bbl can be hung from that to an appropriate level and the soln applied as well. A dowel inside the muzzle used to keep control of the swinging bbl so you can apply the stuff smoothly.
Then unhook and place aside some where where you don't run into it in the darkened shop when you first walk in (I never did that of course).
If you are rusting w/o the breech pin in place, simply use a threaded bolt of that size with a hole drilled X-way in it as both a handle and a place to recv a hook at the breech end while rusting. It doesn't have to inserted very tightly.