10k I would hope would work as a stand alone. But not finding any that can handle conductive surge like the Lincoln welder- as per the the companies tech services I’ve tried- Aimes, Growatt, EG4, just won’t handle it long term. They might initially but hammering the coil systems that use copper plated aluminum coils usually ends up not handling it over time.
Did you find anything? I would advise to put emi filter between inverter and welder. Welder could send nasty noise back into inverter causing problems. Sometimes unit will trip and sometimes it could go boom.
You are trying to make the tail wag the dog.
Chuck that welder in the scrapyard and get a small inverter welder or engine drive.
It will be much cheaper and work better.
You can get a chinese inverter welder that will burn 1/8 7018 nicer that that old buzzbox for about $100... And it will only use 15 amps at 220 instead of 80