It sounds like you need to step up to #2 or maybe #1 polish. One of the nice things Griot's polish and the Porter-Cable polisher is it's nearly impossible to harm the paint. You were right to start with #3 and see if that removed the swirls. I'd try #2 next and see how that works out.

Here's my routine for polishing the 4Runner and my BMW.

1. Wash the car (Duh?)
2. Dry it off
3. Clay with Speedshine and many scratchfree cloths
4. Polish with #3 polish and orange pad (#1 or #2 polish if required)
5. Very heavy coat of Best of Show put on with red pad. Leave the wax to cure overnight. Wash out the pad and dry.
6. Another coat of Best of Show. Buff to a haze.
7. Buff of the haze with 100% cotton polishing cloth.

I keep my cars garaged, so this is only a once a year routine. My normal, once a month is Wash, Clay, Best of Show. Keeps 'em looking sharp.

Hope this helps you out.