I've been one of those black powder Cowboy shooters.
The easiest way to get the plastic out is to shoot a few squirts of Windex down the bores to fully wet the fouling. Wait 5 or 10 minutes and wad up 1/2 paper towel for each barrel. Shove the paper towels through with a rod, repeat if necessary then clean and lube just like you would after shooting smokeless.

Bob