Friend of mine uses Schwartz oil less compressors and has in general found them to be fairly reliable with the exception of the connecting rods fatiguing, I have repaired them several times, and found some interesting failures particularly with the crap we bought on ebay that were "rebuilt" by someone who didn't know a gasket is needed to set top dead cylinder clearance.
The motor pulls 13 amps no load, increasing to 15 at 80-90psi on the tank. (1hp, 120v connection) -this is utterly terrible.
I would speculate the power factor is pretty low. You can certainly go the vfd route with a voltage doubling 120v vfd driving a 1hp 3 phase motor. It will work, but your actual gains are nearly zero. the reason why is because the vfd draws a power factor of about 0.6, maximum of about 0.7 for a voltage doubler.. the problem being it won't last long. the capacitors blow up. (and unlike a motor, you can't add capacitors to get the power factor back up, because its not a phase shift, but rather the vfd draws short spikes of current well in excess of the rms amps)
The motor increases from as low as 70% power factor 60% efficiency.. to 80% efficiency for a 1hp 3 phase motor, but the vfd can only be guaranteed to be 0.6 power factor.
But adding the right amount of capacitance to the motor, will decrease both no load and full load amps significantly, for nearly free and will last 100,000 hours where as a cheap vfd might last a few years.
there is another solution: call up your local hvac companies and ask them for these types of motors:
more often than not, you can take a few broken ones and get one that works. the magnets fly off and crash for example, leaving the inverter good.
https://www.supplyhouse.com/Carrier-S14S0016N01-120-240v-1-ph-1-HP-1250-rpm-Motor -there are several similar on ebay right now for $150 to 250.
The problem is.. it will be 1hp actual. no 50% overload available.
You may find your "1" hp air compressor is drawing 1.5hp shaft power just before it shuts off. that's why the shwartz oil free compressor i mentioned is pulling 15 amps. If the motor was producing only 1hp (assuming efficiency and power factor are the same) it would be: 64% power factor and 64% efficient and would probably burn up. In reality the motor is probably .7 power factor and .7 efficient and it is developing 1.2hp. Or 80% power factor 70% efficient and its developing 1.3hp.
anyhow if you want to get your line amps down below 10 at shut off and develop 1 shaft hp.. you need to get a 2hp motor, wire it for 120v, add some power factor correcting capacitors, and reduce the line voltage to the motor by 10-20% and set the pullies so the compressor only draws 1shaft hp actual. not "nominal".
Ihe inverter ECM motors can deliver 1hp at 10 amps on a 120 circuit because the motor is 90% efficient and the rectifier 70% power factor. 1200 x .9 x .7 = 746. --- you ain't going to get a 1hp 3 phase induction motor to operate at 90% efficiency. maybe 80%.
sorry for the long post...