Think P21S do more than just wax acutally
But yes, try things moving up in their abrasiveness, so claybar, AG SRP, PB SSR2.5/3 or maybe (heaven forbid) a touch of T-cut.
All I can see Halfrauds saying is that it will need spot respraing, so may as well give it a go yourself with polish. If not I am sure they will do a good job, they contract it out to companies so sure it will be fine
EDIT: Nice one, glad to see its sorted!