Yep, 3M PI-III MG REMOVES swirls w/o fillers. It's the next one down, their FG that has the fillers and carnuba. I know the line well and used it in bodyshop applications.
Used 3M quite often, but once I got the hang of Menzerna, it cannot be compaired. 3M may have a huge marketing department, but Menzerna makes up for that in quality of abrasives and binders used for the polish formula. It's just far superior to 3M. Problem is that 3M has a market share in the auto repair industry. Try to find Menzerna at a bodyshop supply house. Next to impossible. That's why I have to order direct from them to obtain quarts/gallons of the polishes. Since I use a rotary majority of the time, I use the Menzerna line for all work performed. If I use a PC, Meguiars or other polishes work well.
Try removing swirls form the new Ceramiclear type coats. Once they are in the finish, it's a PITA to get out. Menzerna made two polishes specific to the new harder finishes, one has more of an expensive abrasive in it, the other a bit less. Works like magic on these finishes! Damn, you think Audi paint is hard?? Try a MB SL600 with that new finish! :scared It's like polishing a stone! Don't ask me how it got marked-up, dealer just wanted it done ASAP for delivery to a customer.
Regards,
Deanski