Howdy,Lucky!I wpoldn't worry too much about the internals.I used to shoot Uberti clones before I switched toVaqueros. At my first three day match, I fired almost 150 rounds of Black Powder through my pistols. I cleaned the barrels and cylinders at the end of the days shoot, each day, but waited till I got home to break them down. I was pleased to find they had NO fouling in the internals to speak of! I have done the same with my Rugers a couple of times, but there is very little fouling that will get into the action. The worst will be around the hand and the slot in the recoil shield where it enters the cylinder area. Usuall I will clean the barrels, the cylinder, then squirt my cleaner into the slot to blow the soot out. Then I will dry it out with WD-40 to displace the water. Oh, by the way, I use a water/soap/Ballistol mixture as a cleaner. Also, Carburator cleaner makes a good cleaner to blow the internals out and it drys fast. When I use this, I follow with a dose of WD- 40.
Some of the top shooters simply remove the stocks and drop the frame into a pan of warm soapy water while they finish their other guns. This works too. Blowing out the action with an air hose or using a water displacement oil is a must, though. Good luck, welcome to the Dark Side, as we bp shooters sometimes call it, and keep yer powder dry!