Working up the load your rifle likes best can take a while, there are just so many variables, ball diameter, patch thickness, patch material, patch lube, powder type, powder charge, cap type, swabbing the bore or not, just to name a few. You really need to keep good notes on your progress and things will change as the barrel breaks in.
But as a generality, I'd not expect much from .010" patches. T/Cs do have very shallow grooves so the recommended combination is a thin patch with a tight ball but .010" is really thin. You might try it with a .535 ball but .015 to .018" would be better. Yes, that will require a hard swat or two on the ball starter to get it past the crown but once the ball is imprinted with the rifling you'll find it easy enough to run on down, since lead is non-elastic and once sized to the bore it remains sized until fired.
For general range work, target and plinking there is no commercial lube that works better than plain ol' spit. Pop a patch in your mouth, get it good and wet, pick off the flakes of chewing tobacco and go for it. I cut my patching at the muzzle which assures a uniform patch with no excess material wrapping over the front of the ball and I've never found the pre-cut patches to shoot nearly as well, nor are they really convenient. Getting a patch out of the plastic bag, separating one from the others, picking off the loose threads, lubing it, getting it centered, all takes longer than laying a strip of fabric across the muzzle, starting the ball and slicing off the excess fabric. You do need a very sharp knife though. A tight patch and ball combination with spit lube swabs the bore with every load so that every shot is from a clean bore. Last Sunday I fired a 25 shot match and never swabbed the bore once. I only took third place but I am very shaky to be shooting an offhand match. After shooting you can clean with spit patches as well as any commercial product and better than most, all of the products of combustion are water soluble and nothing works better, they just cost more and that is the reason they are produced and advertised with great claims.
Pyrodex is not so good as real black powder but is OK in cap locks. If you are getting hangfires due to the ridiculously small flash channel T/C drills from nipple to chamber the finer grain "P" type may do better than the large grain RS.
