+1 for using more pads - neither compounding or polishing is a one pad affair!
If you’re a professional doing this for money, it sounds like you should look into a forced rotation unit like dwaleke mentions. The Flex machines especially are very popular with folks where time is money as you can work through a job without worrying about pitch perfect technique to maintain pad rotation (thus: correction). Rupes and Makita also have forced rotation machines.
If you’re having trouble getting pads off your backing plate, try sliding a popsicle stick or something similar between the pad and plate to start separating the Velcro so you’re not pulling on the foam risking damaging your pads. If your backing plate/pads bond that well, maybe you could put a small piece of tape at the edge of the backing plate to give your finger somewhere to slide in to start separating them.
The moments spent changing pads will pay off greatly both in the quality of results and the speed of cut of a fresh pad.
How many pads have you been using per step?
Also, to answer the title of the thread - I’m a hobbyist and I use 2 machines. I’ve got a Griot’s G9 (DA) I use with both 6.5 and 5.5” pads (and appropriate backing plates) as well as a G8 3” (DA). Just upgraded to the G8 from the previous generation; it came with a 2” backing plate as well so I’ve now got a lot of options to match the machine/pad to the area getting corrected.