Actually, there have been a couple recent Threads that documented very impressive results of cleaning shotgun frames in a good ultrasonic cleaner. What was most impressive to me was how the cleaning brought out a good amount of case hardening colors that were obscured by grime and patina. Those colors were there all along, but you would not know it to see the "before" photos.
For that reason, I would avoid any more agressive methods that might remove any remaining case colors along with dirt and rust. I'm not 100% certain, but I believe that a mild acid like vinegar would also degrade any remaining case colors, so I would avoid any acids (or caustic solutions) until I was satisfied that there were no case colors present that might be unintentionally removed.
