You are correct to worry, typical surge will be multiple times the steady state current. At zero rpm there is zero back emf and the resistance is very low. It would be hit or miss with a smaller converter. While I ended up not installing it permanently I did some experiments with fridges. Mine took 275 watts when running, bar fridge size. I used a 1000 watt psw inverter. Use a low resistance connection, the surge on mine was indicated at over 800 watts. As noted above msw does not work well, the motor inductance will reject a lot of that power and it will circulate until it ends up as heat.
I had good results with that 1000 psw watt unit which I've used for various purposes for 2 years. It is very reasonably priced at Canadian Tire when it comes on sale, which it does every 6-8 weeks, like 40% off. You can set a notice on their website to tell you when it is on sale.
1000 watt inverter
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Ford Explorer or Chrysler 300C to tow with.
Tracer Air 238 to be towed.
Triumph Thunderbird Sport - with the toy-hauler gone it's at home.
Retired very early and loving it.