It can be done pretty quickly, flush some water through the barrell and run a couple patches through it. Still not something I'd want to do while being shot at though.
Also, the thin walled barrel could become very hot. The embers in the fouling caused the powder to flash as it was poured in.
Biting off the end of paper cartridges leads to a mighty thirst. If there was no water in the canteen, urinating into the muzzle was the only option. That alone was an argument for breech loaders.
Sponging between rounds for muzzle loading artillery cleans out fouling. #3 stoppers the vent, which causes a vacuum as the sponge is removed. A very resonate "Phoomm!" sound as the sponge clears the muzzle indicates success.
Civil war & modern practice is to use a damp sponge . Too much water can cause the fouling to crust over leaving a live ember that can last up to seven minutes.
The persistent embers are why NPS, State Park & responsible gun crews do not indulge in rapid fire. Annually it results in premature detonation that causes terrible burns, traumatic amputations & death.
Historic examples:
1540
Premature Ignition. Francisco Vazquez de Coronado's expedition pushes from Mexico as far east as Kansas. En route a No. 1 man loses his arm as a result of a premature ignition of a cannon.
1811
Premature Ignition. Portugal. No.1 man blown from the muzzle and into the harbor along with rammer. No. 3 stopping vent gets severely burned hand.
1840
Premature Ignition. U.S. sailor killed while priming the vent directly from a priming horn.
Nothing new about the dangers of firing blackpowder cannon.
Around here there is a very amusing tale involving an infantry muzzle flash & a well known long beard. Don't know how true it is, but I have seen clothing set alight by flying bits of cartridge paper during a skirmish..