I suspect the total "unloader volume" in most home-scale compressors is literally just the volume of the usually copper hard line that runs from the compressor head to the unloader valve mounted at the tank. The OP's compressor is pretty tiny, that might just be a 3/8" ID line 12 inches long, so total unpressurized volume might be a scant single stroke of the compressor piston.
If this were me, I'd be shopping for a replacement motor, or even easier... a complete replacement compressor, that can be configured 240 volts. The other option, but generally less useful for other applications, is to find an odd 120V-only generator.
And like 404nouser already said, rotating mass is your friend. Some generators actually have a heavy flywheel, which you'll notice by greater than usual disparity between peak and average load ratings, and that would be ideal for this type of load if the flywheel were actually heavy enough to really matter. But I suspect most portable genny's don't have much flywheel, as it would create a portability challenge.
An inverter generator in this application is not only wasted cost, but counterproductive.