I have a similar issue on my cockpit
floor where a rubberized antiskid paint had been applied several times. I began to remove it with grinder and it was.nasty so switched to heat and knife. Only removed part of it. Push came to finish color change on topsides and get sailing so painted over knowing Id have to comeback. Well now the deck
with full removal
looks fine and area where rubber finish was intact has cracks fron expansion contraction through the new finish (System Three 2 part Poly) Be sure the finish you use can match the coefficient of expansion for the non slip or similar issues will probably develop good luck!