And yes, if you engine was running well before, it is not only possible to push start a standard shift ZX, but easy. I've done it on level paved ground using only one foot, with me sitting in the seat. Depending on the source, it is recommended to use 2nd gear when push starting, but I've done it using 1st and 2nd gear, with little difference in the result. With the tranny in neutral (if you are by yourself with no help) and key in RUN position, push as fast as you can, jump in clutch it and shift to your gear of choice, and pop the clutch up quick, being ready to push it down again quick if the engine fires off and runs. I did this periodically during the 50 miles it took to get my 83Turbo home from the seller's house. I was not used to the very sensitive clutch, and kept killing it, and the ignition switch was not working right, making it hard to engage the starter.
Have you tried applying +12 volts directly to the starter solenoid? Sometimes ignition switches can be restricting the volt/amps going to the solenoid, which can make it spin without engaging the flywheel. Get an 8 gauge length of wire, clamp one end to the battery positive post, and with the tranny again in neutral, try just quickly touching the other end of the wire to the same threaded stud that the ignition switch wire is attached to. Doing so should make the starter engage and crank the engine without starting it, unless you also put the key to RUN. If you get good cranking that way, then you have a wiring problem other than the starter. TonyD has posted many times about adding a Ford Starter Relay to eliminate the voltage drops in some cars, to get consistent strong starter action. Do a SEARCH about it, if my suggestion of the external wire helps your starter to work.