You can try series resistors up until the voltage drop is too much, as an isolation from the inductive loading. But the inverter may burn up in a years time like mine did. Mine was an APC 1300 VA and it seemed to have ample power, but in 6 months its step-up converter burned up.
I talked with an APC tech who seemed annoyed, as if he had this issue all the time. This issue turned out to be the way AC motors and especially AC motors with start capacitors not only hit the UPS with a reactive load, the capacitor causes a phase shift in the waveform based on uneven current loading, in spite of the UPS attempts to maintain a sine-wave.
Even though the UPS was rated 3 times the refrigerators maximum load, it was not a balanced load. The typical UPS, sine-wave or not, is meant to drive wall-wart transformers and switch mode power supplies which have dynamic resistance, but little reactance.
I thought something was wrong when I noticed the UPS seemed to be constantly charging, especially after a power failure then the power comes back on. Yet the refrigerator was no more of a load than my stereo with the volume cranked up. The APC tech warned me that big audio amplifiers have a big transformer that can cause stress on a UPS.
The ends result is I run the refrigerator and stereo directly off the AC outlet. My only option was to buy an expensive generator which ignores asymmetrical loads.