Two phase is equivalent to 3 phase, that is why they can be converted one to the other with just passive transformers.
Using a capacitor phase shift will kinda work, but has essentially the same issue as a "static phase converter", you lose some motor power.
Another issue is that the optimal size of capacitor is not a constant, but depends on load. So whatever you choose will be wrong for a lot of the motor's power range. And, the capacitor can only provide a real 90 degree shift when there is a lot of voltage drop across it, vs across the load. Otherwise you get a lesser phase shift, and again, reduced power.
The only way to get that large voltage drop is to do like a steelman converter, and run the shift capacitor from a higher voltage, using a boost transformer. In fact, the Steelman system would work.
If you really do not need full power, you can essentially just use one winding to start, and drop it out entirely for running, using just the other winding. That will be very like a static converter, but you will be limited to 50% power.
