"How do you remove the 'batwing' TV antenna and maybe the inside crank
without removing the whole unit and leaving a large hole in the roof?"
On the roof there's a pivot pin holding each of the two antenna support struts to the base. The pin is held at one end by a c-clip. Remove the c-clip with a needlenose pliers and then knock out the pin. Repeat with the other strut's pin, then cut the coax cables, and you're done! The whole antenna assembly can be lifted off the base and discarded.
The inside crank is secured to its shaft by an Allen (hex) head set screw. Loosen the screw, and the crank, spring and washers can be removed. A white crutch tip (available in any hardware store) is a quick way to cover up the remaining shaft, or you can hacksaw it off flush with the ceiling.
If you choose to cut off the shaft flush and remove the entire pointing knob assembly as well, check your local hardware store for a 4" round dent protector/cover (usually found in the locks-and-doorknobs aisle). These thin, textured plastic disks, available in white and ivory, do a great job of inconspicuously covering up a large hole.