I have THEORIES on why this isn't working. They are UNTESTED and
should be used as food for thought.

I have a 10 horse motor phase converter. I end up with 220 volts
across two windings of my milling machine, and with 209 volts on the
third leg. When an amp-probe is set on each leg of power to the mill,
the two legs going to the 220 V single phase have large amounts of
current in them, and the generated 3rd leg has essentially none. I
think that the generated third leg is more startup than run. Any
amount of 3rd phase is better than none, and gets most motors running.
Motors running off these home made rigs run mostly on single phase, in
one winding.

I suspect that putting a step up transformer on the home-made third
leg, to boost the voltage where it matches the other legs would make a
large difference in the amount of power delivered, and hence increase
the starting torque. Never tried it, since my mill starts, I am happy.

I also suspect that the only hope you have on your present setup is a
pressure relief valve which unloads your compressor until it gets up
to speed. I think these devices are available commercially.