How to determine (not estimate) starting amperage of a motor?
Measuring the startup load is as easy as using a clamp on meter and turning the air handler on and off.

The startup load will be high for a split second, then drop down to a steady load. 

Use Ohms Law to calculate the wattage.

Watts/Voltage = Current

As mentioned in my comment, the invertors peak load is a good indication of the invertors motor starting current.

Edit

To get the most accurate motor startup load readings from your meter, you may need to use one that supports "in-rush" readings.

Meters like the Fluke 374, 375 and 376 support "in-rush" readings.

Edit 2

I did some digging around and found the formula to calculate inrush current.  

Take the NEMA assigned letter to your motor, in which case yours is letter B, and plug that into this equation:


  Iinrush=(code letter value X horse power x 1000) /( √3 X Voltage)


You can ignore the square root of 3 if  your voltage source is single phase.


  in-rush = 3.54 x 1HP x 1000 / 120V = 29.5 Amps


Bottom line is your invertor needs a surge rating of at least 4000 Watts


  4000 / 120 = 33 Amps


NEMA Motor Letter Table