Thats what we did here - We got the AIMS PSW 600WATT Power Inverter PWRI60012S from AMAZON ($159)
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This has two 120VAC outlets and I ran a multi-tap extension from the Power Inverter to the Home entertainment area and to a night table area in the bedroom.
I can plug in any low wattage 120VAC item into these multi-tap cords without worrying about going up in blue smoke... Anything that has motors or electronics will get hot and make humming noises when hit with MSW type power inverters...
Been there done that as well... Why chance it for just a few dollars savings... In the past the PSW Inverters were very expensive. Not so anymore...
I haven't tried the fridge on the 600WATT Power Inverter but it just might be strong enough to get the initial start going. I am pretty sure the 300WATT Inverter will not work starting the fridge.
Roy Ken