Sounds like you don’t have a crazy amount of fabrication tools on hand, but I’d probably grind the head of the leg bolt as plat as possible then use a unibit to drill the head worm until the head is all but gone and the leg pops off. Then use a punch and drive the remaining stud into the cabinet and replace. No cabinet damage. No leg damage.

Attempting to weld inside the cabinet won’t end well. That’s 30-40 year old wood that’s brittle and stressed. It won’t catch fire like some kind of inferno, but the heat from trying to get the press but reattached to the plate would do some noticeable damage.

Just be calm. I’m sure your buyer understands how this stuff goes. If you drive 4 hours for a game, this ain’t your first rodeo. The buyer may have an idea or skill set.