As all above have said you might want to check into just changing the motor.

Static converters have come a long ways in the last 20 years. The old ones were nothing more than a passive phase shift network to improve starting torque. Once rotating the motor was in a single phase mode for all intents.

Modern static converters are completely different animals, and are more properly termed VFD's (Variable Frequency Drives). They rectify (convert to DC) the incoming single or three phase voltage, then chop it back up to form the required AC supplied to the motor. They are/can be programmed for a soft start along with a speed that would limit the actual draw on your single phase power.

Not cheap, $250-500 (new from Graingers) for a 1-3hp single phase to three phase drive, but if the compressor you bought is of decent quality this may be the best approach.

Several are on ebay, just be careful in matching the horsepower and voltage requirements.

Cheers, Mark