My option would be for a pro polisher to do it!
Actually several folks at the vintage trailer rallies with very nicely polished trailers - read NO swirls ever - have used & recommended the services at the truck stops who polish those big tanker trucks you see on the road. I've never seen any swirls on them, but they use very large wheels on edge - rather than the Dual Action (DA) or double DA of the Cyclops unit.
Their polishing materials & techniques also seem to last far longer than the Cyclops & polishes they recco, up to 1.5-2+ years & still look great, & they're easier for the owner to keep up!
And they don't charge the $100-200+ per ft of trailer (including A-frame) that the TT polishers charge!
I think the reason their technique works as well - if not better - than the DA/Cyclops technique - is that they keep all of the buffer action in one linear direction due to using the edge of a 36" diameter or so buffing wheel (rather than round-n-round with or without DA & random orbiting), usually vertical on TT & tankers I think.
From my experience in Porsche club (PCA) concours car shows, what we teach the entrants for polishing & waxing & detailing/finishing their cars, is to keep all of their action linear & to the length of the car - in order to control the reflections to not pick up those round motions & fool the sunlight - or at least we judges' vision of it when judging!
Anyhoo - if I were the hubby in for this "selfless gift" - a pro polishing of this type would be more welcome .... unless you're the type who appreciates a washer & dryer or the like for gifts!?
I know, I know ... this is heresy amongst the shiney trailer crowd, but there is actually a similar difference of opinion in the shiny airplane crowd where the Cyclops "sells" itself, with this on-edge wheel buffer polishing technique, as well as with TTs.