PJB - .010" patch in a 12 bore is a VERY thin patch - too thin to hold enough lubricant. If you cannot use a .018" to .020" patch, you would be better off using a .690" ball and a substancial patch - one that will hold enough lube.
: Recently, I've switched over to using LehighValley lube, available at Trackofthewolf and other places. It has exceptionally high lubricity, and keeps the fouling soft - no cleaning necessary until one wants to clean after shooting is done.
; Tinker - Moose Snot - I haven't used it for well over a year and find that pure neats foot oil, mixed with castor-oil 50/50 worked about as well. Some guys use only neats foot oil. Note, not Neats Foot Oil Compound, but pure neats foot oil. Best of all of them in my rifles now, is LehighValley lube. It is ever more accurate than spit, which I've used for competition for over 30 years - now, it's Lehigh Valley lube only.