I would just hit it with some M205 on a white pad, speed 5. That should knock down most of the light swirls. Perform a test spot. Be sure to check your work to ensure the results you achieve are up to your standards. Then you could go straight to a wax or sealant.
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I use Mike's method of cleaning your pad on the fly. I get an all purpose towel and place it over the pad after you finishing running the machine in the pad washer. Then grip the pad and turn the machine on speed 1-2 and it will dry out fairly well.
Hammer, it sounds like they are Lake Country Flat Pads. If the white is more firm than the blue they are. The white is used for polishing and the blue can be used for applying sealants and waxes.
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Cold! High today of 15 degrees. Woke up to almost negative temps.
p.s.- Seeing this title I thought it was an introduction thread and wondered if we had an rwright imposter!!
From the sounds of it you would have to rip up the whole carpet to get it almost perfect. I know there is a thread around here about a car that water leaked through the sun roof. So I would look for that.