130304-1215 EST
If it were my own installation, then I would do this:
Size the wiring and breaker on the 3 phase side based on the NEC requirements for the 6 HP worth of load. This implies I would use a breaker on the output of the phase converter.
On the input side of the phase converter I would assume a power load of 8 kW and a PF = 0.8 . Thus 10 kVA. Size the 240 supply at 10,000/240 = 42 A. The only question will be if a 50 A breaker will tolerate the phase converter inrush, and will voltage drop be so great from the inrush as to cause startup problems with the phase converter.
The phase converter is simply a mechanically unloaded three phase motor excited as a two phase motor with one coil directly connected to the single phase source, and a capacitor to the other motor terminal to supply a phase shifted current for starting.
The phase converter needs to be started with no electrical load.
Note: above I assumed quite a bit of excess power over the 6 HP (4500 W) of maximum load power. Also have assumed a rotary converter. If you can find a used converter there should be a big cost saving, even if the bearings need replacement. Your description might imply a home shop. Also I doubt that a 15 HP converter is needed.
Anyone else have other suggestions?
If there is really a power source problem, then get a converter with an external shaft, then use a rope pull method to start, or a small motor to bring the converter up to speed, and then apply input power.
.