You would clay before polishing so getting a pro. detailer to "sort it" should include claying as part of the pre-polish cleanse routine. You certainly wouldn't then clay it again after polishing (well, not for another 6 months or so), and you should be aware that clay can itself mar the paint so it may need polishing again after you've clayed it.
You might want to consider a filling glaze in the mean time. If you want to have a crack at it yourself, you can (not necessarily will) get a half decent finish polishing by hand (it certainly won't be perfect though as Ekona mentioned), you could then use a filler heavy glaze to hide the remaining swirls before sealing and/or waxing. Obviously this option is a temporary measure as the swirls will still be there when then glaze wears off.
Hmm, I ideally want a permanent solution and fix so a filling glaze isn't really an option.
And I don't fancy using a machine myself as clearly even the dealer didn't know what they were doing so I would only make things worse. Alot worse hahaha
It may sound daft but do ding master etc not use machines to polish etc after they've sorted out a nasty dent or anything?
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