I use Autosol and a microfiber cloth for my Henry. If you want a swirl-free finish, successively finer polishing grits are the only way to go.
Yeah Solvol Autosol is the stuff!
Used the Flitz, used the Never Dull (might be a second place pick) but AutoSol and a soft clean cotton rag was always the last step in making shiny sh1t SHINY!
I did a LOT of shiny sh1t for retirement presents and posting presents at the last unit I was in in the Forces, and I can say that among other things, a set of MicroMesh padded abrasives (Up to 14,000 grit) and AutoSol for the last step.
One key thing I learned, is that you can go an awful long way up the grit scale, and still see swirl marks, if you are swirling the polish around. You want to keep the scratch pattern running in only on direction. When you step up, use that same direction, and if you get to a point where you think you are done with that grit, then do the next. You only have to back-step one or two grits that way, if you are not satisfied.
Worst case is that you only see marks in one particular angle, rather than from all of them.