I've been doing cowboy shooting for almost 20 years and a lot of the BP shooters use plastic wads. They either straight Ballistol or a Ballistol water mix. They give both barrels a couple of squirts and after about 10 minutes run a wad of paper towel which usually pushes the plastic out of the barrel all at once.

I use fiber wads & BP, but I do find the sooner you clean the barrels, the easier it is to get the barrels clean.

I have become addicted to English hammered shotguns to the detriment of my wallet.