The Zoomatic throwoff mechanism employs reverse thread 10-32" threading. Often the threads are stripped out, either from misuse or from road injuries over the years. I have yet to find a source for these taps and dies, other than to contact a local tool and die maker and have them made as a custom order. If anyone knows where they are readily available for purchase please do let me know. Otherwise I suggest that it is possible to do a "retro-repair" for far less expense utilizing normally threaded parts and pieces selected from various vintage makers' tone control and snare throw parts. I've had excellent success replacing the original knob and rod with Ludwig and Slingerland vintage tone control parts from the 1970's, and many of the 1960's/70's vintage Japanese strainer mechanisms employed threaded shell mount receivers of the same design as the Zoomatic. Most likely you will end up choosing from among normally threaded 10-24", 10-32", or 6mm x 1mm rods and receiver mounts.
Remove the throw and shell mount receiver from the drum, disassemble the knob/rod assembly, and lay out all the pre-selected replacement parts and pieces to check for compatibility and fit prior to reassembly and remounting the repaired throwoff. The trick is securing the threaded rod to the inside rear of the casting so that it is secured and functional while not restricting the motion of the lever assembly through which it passes. This isn't really all that difficult with the right flat washers and some locked down square or hex nuts. The original receiver mount on the shell itself will likely have to be replaced with a retro-fit piece of similar appearance and function. Takes imagination, some small hand tools, and a little skill. The only other option I can suggest is to buy a complete and intact vintage Zoomatic from another collector. All the best!