There are very few soft starters that are going to tolerate being fed from a rotary phase converter. Although the capacitors on the RPC will make the voltage APPEAR normal on a meter, and the differences are not as big a deal directly on an induction load like a motor, a soft starter has to deal with things like current rise times etc. The charging current of a capacitor has a very steep wave front as far as the SCRs are concerns, much the same as a dead short. What can happen is that the high dV/dt (change in voltage over change in time) can cause SCRs to "self commutate" meaning they fire on their own, i.e. when you don't necessarily want them to. Once SCRs begin firing at the wrong time, the Soft Starter loses track of what's happening and, if it's good, shuts down to protect itself. Cheaper ones just blow the SCRs.
You can try adding a reactor in front of the soft starter, the added inductance in the incoming supply may soften that capacitor charging current rise time as far as what the SCRs see. That will of course drop your throughput efficiency as well, but may be your only option. If you can, borrow a suitable transformer somewhere that can be configured 1:1 and temporarily hook it up to see if it helps. If it does, the reactor will work too and they tend to be cheaper than transformers.