Give the Ultimate Compound a go first, using the yellow polishing pad at speed 5 and a good bit of pressure. Move the pad very slowly over the paint, and confine your work area to no larger than about 2' x 2', maybe even just 18" x 18". I like to tell people to put enough pressure on the pad to stop it from rotating, then ease up just enough to get it spinning slowly again. And it will be spinning very slowly indeed.

If you find you need to move to the cutting pad, keep in mind that it may well haze the paint while removing the swirl marks (and that haze should clean up easily with a follow up of the same product on a polishing pad) and it might get really hot where the pad meets the backing plate. Looking at the motion of a dual action polisher the free rotating spindle assembly allows for full random motion, meaning the pad is constantly changing direction. Now looking at how the hook & loop of velcro works, you can see that the pad is constantly trying to break free from that hold. And that can generate a lot of heat on the velcro. So much so that with constant use it will start to break down the adhesive holding the velcro to the pad, or even the foam itself. This can lead to total failure of the pad. We see this with our pads, and with the Lake Country pads - it makes no difference. I've measured 231 degrees F in that area, with product literally starting to steam. That's not good! So keep the above in mind in the event you feel the need to reach for the cutting pad.