You should ask about balancing capacitors and phase angle correction
capacitors.

Hm, I thought that you did not use capacitors. In any case, yes, it is
a great issue to ponder, but I cna do it after I get the actual motor.

This is different than start capacitors. Call it fine-tuning
the output.

Also you really should have at least one contactor in the setup
which will drop out (self-holding) if you lose power while the
converter is running.

Do you mean that the contactor would open a 3 phase circuit of the
power is lost on the 2 phase circuit?

Nitpic: It's center-tapped single phase, not 2-phase (which
requires 4 wires and has the sinusoids at 90 deg to each other).
It just looks like two phases because we measure from the center tap.

The contactor is to keep the motor from trying to restart on its
own without the pony motor. A lot of people put them on saws,
lathes, and milling machines for the same reason (so sudden starts
under load). This is regardless of phase.