Ok gang. There is no reason to reinvent the wheel.
These jags, patches, etc have been used with little trouble for at least the last 150 years.
Been doing this myself for the last 50 years. Never turned down a jag, never got a patch stuck. Can’t imagine our forefathers had these issues either.
Sounds to me like hard dry fouling. First pass, very wet patch, or water rinse first, then mop it out. Should be VERY little resistance.
If it’s getting stuck now, then go look for something that snags the patch.
P.S. those patches are way too dry.