Have you tried glass cleaner (windex type stuff?)

otherwise, disassemble the pedal and take the enclosure to an automobile dealership that has a paint booth and inquire how much it’d be to get it clear coated.

I don’t see anything wrong with that for cleaning; but would highly recommend that you not use any cleansers that are abrasive, are alcohol or amonia or oil-based, as they would be very likely to affect the paint.
Dawn is a mild cleanser and water-baed but also great at getting dirt and grease off of things, but i would not think anything with amounts of liquid, even water is a great idea if it might leak into anything. so spraying is out. i use a Q-tip, and a small soft cloth to clean my pedals, and a little mild soap (like dawn) works ok. the casings can rust, so they have some iron content, so avoid moisture in general. Turtle wax isnt a terrible idea to protect it, but be careful of other types of auto polishes or car “waxes”, and they often have small abrasives, or are made of silicon and or oil-based. neither is a good idea for electronics or these kind of paints.
For and old tired looking DEM pedal I used a little bit of Flitz metal polish also is a great rust remover (its for metals, fiberglass, plastics) and it worked out very nicely. At first i was just trying to remove some small rust spots on the top by the lettering, but i noticed it cleaned the metal and the rust, so figured i’d do the rest of the metalic part, but noticed it didnt seem to affect the inked lettering, so tried a little corner of the main paint art on top, and it didnt damage it, but it did give a bit of a more even luter to the whole top. Flitz removes rust and dist, but also polishes and protects too, so waxing afterwards isnt really needed. it doesnt feel oily or waxy or anything after either. I have also used it to clean rusted or corroded mechanical type electrical connections too.. (like guitar jacks, amp jacks.) For those i usually clean it iwth the Flitz so its silvery metal again.. then use some rubbing alcohol on a q-tip to make sure there is nothing left on the jack, then its just clean metal. an electrician once told me you should clean the jacks and connectors on your amp and guitar now and then to keep a good clean connection..youd be surprised how much grease and dusty dirt you can get on those parts over time. later on i just added the metal cleaner to the practice.