Matt,
looking at your pics again, I would say that not much cleaning on the action is needed, apart from perhaps the area under the horn trigger guard.
Don't forget to lightly oil he surfaces after cleaning with rubbing alcohol (teaching my grandmother to suck eggs! - hehe)
I attach a couple of pics of my 1939 German BBF (only one shotgun barrel on top of a rifle barrel)for comparison.
I have not particularly cleaned the surface of the action as I think the contrast looks good as it is; and it is, after all, an old lady & needs to be shown in all her glory.
Regards
Günter
NRA Life 1974

