Two things about coatings-
-Acrylic coatings (which it looks like you have) are NOT suitable for ponding water whatsoever. Silicone is.
-preparation is KEY for installing any new coating. The roof will have to be cleaned, dried, and primed to receive a new coating if you go that route.
The unfortunate part of installing a new roof section over the trouble spots is the inability to “mate” properly with the coated roof. You will most likely need a new roof unless you re-coat with a Silicone.