A patch wetted with a squirt of isopropyl alcohol(buy it at the local grocery or pharmacy) is a more efficient way to clean the bore between shots. At the range and in the field, where practical. One wet patch, followed by one or two dry patches, and your bore comes out sparkling clean. Best way I know to clean a muzzleloader bore. The hardcore traditionalists on this forum might not agree, but you'll soon find that practical is often best, when it comes to muzzleloading. Plus, you won't run dry of spit. Try it and you will see.
By the way, if you have a source of flannel at home(old shirts, nightgowns, etc.) these make excellent patches. Cheap, too. Cut them about 2" square for your .50 cal.
This size works well...you can fold them to make a tighter fit, or leave them as is.
As for jags that spin....unnecessary, in my opinion. When you push the rod down bore, the friction between a snugly fitting bullet or cleaning patch and bore will impart a natural spin to the ramrod. An ordinary jag, threaded onto the end of the rod, will spin along with it.
It never hurts to experiment with as many different bullets or bullet/sabot combinations as possible. Your rifle will let you know what it likes best. Many of the inlines, for example, with their relatively fast rifling pitch(twist), prefer saboted bullets. Once you know the twist of your rifle's bore, it is often an easy job finding the right combination.
I'm not familiar with your Thompson, but many TC rifles feature a twist of 1:48" If so, this rifling twist often work very well with saboted bullets. Good to know.
A very good learning resource for new blackpowder shooters, is Sam Fadala's Blackpowder Handbook. Lots of good information inside.
Muzzleloading is a lot of fun, once you get a handle on it. Takes a while to pick up on all the little things to know that make it easy....but that's the idea behind this forum. Some very knowledgeable people here, who can help. Don't be afraid to ask.