How can I remedy moisture intrusion from my concrete slab?
Other than taking a jackhammer to it and doing it right from the bottom up, (or turning it back into a carport): 

Lay 6 mil plastic in a continuous sheet, place 1 or 2 inches of XPS rigid insulation sheets, pour 2" of gypsum cement (might as well place radiant floor heat tubing while you are at it, even if you don't have immediate plans to use that.) 

A cement slab for a carport almost certainly has no waterproofing below it nor insulation of any kind.