Many of the mopeds were copies of other models w/ their logos sprayed on. Contact HandyBikes and they might know what goes where. A lot of American mopeds were only European mopeds made under contract. The general moped might have used parts from other moped models and assembled them w/ their own logos/colors. That was very common. Someone at handybikes might know. A lot of Minarelli-based mopeds look very similar (unless the manufacturer actually made its own frame parts, like Carabella, but many did not).
Bottom line ... you might still be able to get body parts for them. And Jim is correct, you will always be able to fin Minarelli engine parts and other standard parts.