i compared notes with @kenshirriff who has been reverse engineering a Bendix Air Data Computer: https://oldbytes.space/@kenshirriff/110578423219847109
in fact, the magnetic amplifiers it uses are exactly the same. Ken wrote a very nice article about magnetic amplifiers for the IEEE Spectrum, so i won't explain it again: https://spectrum.ieee.org/the-vacuum-tubes-forgotten-rival
i built my own inverter, natch! this is a junk box 115V transformer with a 12V center tap output. it turns out to work fine at 400Hz. i'm supplying DC to the center tap and there are two MOSFETs each with the drain connected to the remaining two terminals. this is essentially a resonant Royer design, but the MOSFETs are being driven by an Arduino that tries to PWM two half sine waves. it's bad but it works!
the last stage of the transistor amplifier drives the two mag amps, which are cross connected so that one runs the motor in one direction while the other runs the motor in the opposite direction.
depending on when the transistor turns on (due to the phase of the signal from the autosyns) it will turn on one or the other mag amp.
(the schematic here might have swapped wires on the mag amp outputs, so ignore that)