I'll be interested in readings replies here. I just started experimenting with machine polishing my personal airplane, which is a fiberglass (GFRP and CFRP) design with a tough UV-resistant urethane-based paint for a top coat. The existing finish has surface oxidation and some oil contamination.
At present I am using a Mirka CEROS (5" pad by 5mm stroke), Festool buffing pads, and the Festool polishing compounds. In the two underwing and under-belly test patches, the results were phenomenal, going from beat up oxidized paint to a bright white, near-mirror finish surprisingly quick.
Here are the pads and compounds I'm using. Your needs may be different, so take it with a grain of salt. I imagine the results might be even faster with a full size DA polisher or the RO 150. However, I needed something super light and maneuverable, thus trying out the CEROS for this application (lying on my back under the wings pressing upward a 5lb polisher for hours on end didn't sound like fun).
Festool:
493866 6" Fine Sponge (white)
493880 6" Very Fine Sponge (black)
499021 MPA 5000 1-Step Speed Cut Compound
493816 MPA 8000 Polishing Compound
Also:
Rejex paint sealant (by Corrosion-X)
Pad & Microfiber cleaner by Chemical Guys
Microfiber detailing towels by Chemical Guys
I started with a very through cleaning (two bucket method to reduce grit contamination), then using the white fine sponge with the speed cut compound. The next step was polishing compound with the very fine sponge. The final step was hand applying paint sealant. A critical aspect is to prime the sponges with enough compound so you aren't rubbing them dry. Also, it is often recommended to start with the least aggressive steps and see how it goes before getting into heavier cutting.
I found a great thread on this forum on polishing... As well as plenty of information on other web sites such as Autopia, BuffDaddy, AutoGeek, etc. there seem to be many rituals around polishing, some which may even be provable, and some probably not. In the end it all seems to boil down to glorified sanding...
Interestingly, there is a movement afoot to go from 6" pads to 5" pads. I just ordered some 5" microfiber buffing pads to try on the CEROS and see how that goes. I have a suspicion that they should be better matched to the counterweight and all things being equal, 400 watts into 5" is more intense than the same spread out over 6".
I also tried a clay bar on the finish before starting polishing, but it had no detectable effect compared to when I've used clay bars on my cars.
I am no expert in this, but have plenty of experience with manual polishing a la Karate Kid. Wax on. Wax off.