So after trying to use the Craftsman orbital to work on my car and having it throw off every damn bonnet I put on, I said screw it and went with the advice of those here.
Picked up a PC (7346 because they didn't have the 7424; but it's the exact same machine, mine just came with an extra sanding pad).
Used my Adams Swirl and Haze Remover and Fine Machine Polish with the PC polishing pad that came with the orbital. I had used Revive last week-- didn't use the Buttery Wax this time around. Didn't even need to (though I plan to wax it this afternoon; ran out of time, but); the FMP made my car look new again. And-- It was SO easy to use the PC; even for someone who had never used one before!
WOW!!!!! Adams and Porter Cable gave me my brand new car back
She looks SO amazing. My family was marveling at how my paint "looked like a mirror!"
Figures it's supposed to rain today
Thank you all for the tips and advice. Yep, you were right. Adams + Porter-Cable FTW. It was SO nice to not have to spend four hours hand-polishing my car.
Have a look: