Personally, I would remove the existing UV coating if it's starting to fail before spraying a new coating over it. But if the original coating looks okay, then just leave it and don't bother with a new coating. That's going to be your call depending on how they look. I'm not a fan of putting one product over a different product since there could be a reaction between the two.
Scotty also recommended the
Meguiar's PlastX polish to start with as it's a very milt abrasive. Since your lenses are not yellowed, you don't need to cut into the acrylic with more aggressive abrasives. After the disaster you encountered with your sanding disc, you may want to just do this by hand with just a microfiber cloth and the
PlastX. It might take a while to get all the UV coating off, but beats risking the destruction of another lens.
Go slow, check your results, continue until all the UV coating is removed and you have a nice clean surface. Once done, I would also go over the entire lens with dish washing soap and rinse with fresh water to ensure you have all the Plastx residue off. Then a final wipe down with Isopropyl (rubbing) alcohol so it's a clean as it can be before applying the new UV coating.
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