When I use a foam pad and want to clean it, I either use the pad washer (pretty expensive for just an individual doing a single car) OR rinse it in running tap water. After the rinse, I compress the pad to remove most of the excess water, then take a clean terry towel and place the pad inside the towel. Then, I stand on the towel to squeeze the remaining water out and let it air dry.
You can do the same with wool, but it won't dry as fast.
Yes, I would start with wool and work a 2' x 2' section. Personally, I play it safe on the pressure applied to the rotary and make multiple passes to complete my work. The dealer here has 25+ years of BMW paint knowledge and uses far more pressure with less passes than I do. But the results are the same.
Try the following:
Less product, clean pads, work a section until complete slowly, then switch to a softer foam.
Toto