Listen to Wizard and GD.
This is what we have been doing since the DC Norcold died. It is the starting load that is the killer. You do not need PSW, the motor will just run a little hotter with a modified square wave inverter. I ended up with a 750/1500 Cheap Chinese unit and got one replaced in short order under warranty, but they are so cheap that I actually carry a spare NIB.
Put the inverter near the house bank. Run Gonzo heavy cable to the house bank. (The starting surge may be near 100 amps.) Place the inverter where it can get cooling air and not get wet. You can also use it for lots of other AC things while it is taking care of the reefer.
Matt