Apologies for bumping a slumbering thread, but it's new to me.

This discussion reminds me of a YouTube video I saw posted online just a couple of days before the last post here. I will not link to the video here as I expect AvE's language and innuendo would be considered inappropriate but it is titled "Diesel Engine Weirdness | Sailor's Delight".
He could only get his picky appliance to work on an inverter if the blender was running. The suggested reason was that the motor was a large inductor and smoothed the output enough to satisfy the electronics. This wouldn't be a very good solution for something like a cooker that has to run for a significant period of time, but might provide additional data if you're not sure if the problem is the supply or the appliance.