Gary, that's me in the video and I clean it.
With .44-40 and full charges virtually no fouling gets back in the action. The .44-40 case is thin and obturates very well, sealing the chamber. This is a major reason why I bought it in .44-40 rather than .45 Colt, which has thicker brass and does not seal the chamber as well.
To clean the bore I use a water-based cleaner such as Windex, windshield wiper fluid, or Hoppe's MPro-7. The bullets I use carry a lot of lube, so that even after 50 shots the fouling stays soft. If the cartridges are loaded with Swiss 3Fg it takes only three wet patches (using both sides) to clean the bore. Goex doesn't burn as cleanly, so it took 5 or 6 patches.
To lube the bullets I'm using a mix of beeswax and mutton tallow. It does a great job of keeping the fouling soft.
After the wet patches come out clean, I run a couple dry patches through the barrel and follow up with a patch wet with Ballistol.
I'm not exaggerating when I say that it takes less effort to clean the gun after shooting ammo loaded with Swiss BP than it does to clean it after running ammo loaded with Unique and commercially cast bullets through it.
If I rest the rifle on something so that it's horizontal and upside down, the goop from cleaning drops right out the ejection port instead of getting into the action. If the rifle is vertical when cleaning the bore the fouling gets back into the action, so it's a good idea to remove the sideplates to wipe out the residue.