I have a broken Rainbird APAS-100 valve, how can I fix it?
Champion Irrigation makes a valve called the PCL-100 which is compatible with the body from the APAS-100 (and a PCL-075 which ought to fit the body of the APAS-075), which are available as of this writing.

The specific part that I got is the PCL-100-C (not sure what the C means and if the B model works in the same way).

The valve fit perfectly onto the APAS-100's body (though the wires from the solenoid were a bit of a tight fit when installing, I had to take some parts off the neighboring valve to get it screwed on).  In initial testing, it seems to function just fine on the APAS-100's body.