the output you get is always related to ratio of source to load impedance which is the same as load regulation (ratio)
Analyze and you will find the problem
Motor has an impedance ratio of 1/8:1 on startup
Light bulb is 1/10:1 on startup
A resistor is 1:1
A Capacitor impedance on a diode bridge is determined by dissipation Factor at 120 or 100Hz may be 1~10%:1
So what is your inverter output impedance? ( your source)
What is it's source impedance? Does that affect the Zout?
Is it constant?
What is your transformer impedance ratio?
What is your RdsOn?
Now compare that Zout with Rs of motor coil which is usually 1/5th to 1/8th of average impedance Z= Vnom/I_rated at max load.
Keep in mind if RdsOn is switch ON , d.f.=50% of the time, that average impedance = ESR = RdsOn/d.f. or 2x, if on 10% of the time, ESR=10x