There is no way to completely eliminate mold from room-temperature surfaces as mold is propagated by spores in the air and air is carried through the ductwork. You can reduce the abount of mold by sealing and superinsulating the ductwork so the ducts never get below room temperature to collect moisture, but even then after a year or so of running even with a great filter, any dust is a medium for mold growth. The spores themselves are a medium and moisture propagates them.
Get radiant floor heat or flat-plate radiation with warm water heat and keep the surfaces clean. Use a ductless split system and clean the filters and coils regularly. You have a specific health problem that is exascerbated by ducts.