Reddog,
If you are interested in completing the job by hand, then readup on some of Scottwax's old posts. Prior to him buying a PC, he did EVERYTHING by hand.
Look at Poorboy's products ... I'd consider getting some SSR2.0 and see if that does the trick by hand. Also, ScratchX by Meguiars can do a really nice job as well. Check out Mike Phillips (Meguiar's employee) post about how to use it get maximum results.
It might be the case that your swirls are too bad and may need a PC or Rotary.
That orbital you have, unfortunately, isn't really going to be do anything for you with respect to the swirls. You can use it to apply wax etc but it's not even close to being strong enough to do corrective work.
04 ford escape its fire red and a clear coat.
860 10" craftsman orbital with terrycloth bonets. - Only good for applying waxes.
I have mothers original carnauba cleaner wax (decent cleaner but won't address spiders very well)
3m liquid wax ultra high gloss finish - poor durability but does produce a nice look - better products out there.
meguiars mirror glaze#9 swirl remover 2.0
Nice product, I've found it to occasionally act up on me though i.e. tough to remove at times, smirring etc.) Pretty oily so under a wax, it can help with the "wet" look.
Paco