fangster- Ah, those are the two polishers I use for significant correction, all good there (including your pad sizes).
Inspection lighting:
-the sun isn't "creating the illusion of swirls", it's just showing you what's really there (sorry to say). The trick is to simulate that kind of "point source illumination" when you inspect. Generally, you want a single point of light, at a bit of a distance, that's not too bright (too bright washes out what you're looking for). And you gotta a) move the light around until it's at the right angle and b) move yourself around until *you* are at the right angle too. Yeah, huge PIA at times.
-I'm kinda fanatical about my inspection lighting, using halogens, a 3M SunGun, incandescents (regular old "bare light bulbs", even just 60w ones, can actually work great under some conditions), and I'm experimenting with LEDs. I do *NOT* find fluorescents to be any good for this kind of inspection (they're fine for "texture" issues like orangepeel, coarse sanding/paint prep marks, and the like..). And if the weather cooperates I pull it out into the sunlight too (else I have to use the SunGun).
-biggest trick IMO is to turn out all the other lights, so your inspection light source is the only light shining on the area in question.
-getting the illumination and inspection angles just right can be a huge PIA...I often say that I really do spend more time inspecting than I do polishing! But then I'm usually working on silver vehicles and they're especially tough so see minor flaws on.
There are a lot of threads here where we discuss inspection lighting to death...probably worth the dreaded SEARCH as others have opinions/experiences that differ from mine. Plus, there are some really good ideas for DIYing pro-grade inspection lighting.
Get your lighting sorted out, use less product when compounding/polishing, work small areas at a time, and you'll be well on your way to getting better results.