[saiya-jin]

Yeah, i don't think its good idea to move during burnout straight to another job, with high expectations for seemingly senior position, tons of stuff to learn, integrate with new teams/culture/etc.

Just stating a looming burnout and serious will to rather NOT work at all than continue working at that company under current situation should let them realize how grave the situation is. Don't leave them room for interpreting this as 'he just needs a pat on his back and some sweet talk and he is back on track'. Polite and honest, but firm stance.

People are so freaking afraid to be on their own without job for few months. Unless OP's finances are very tight, it sounds like this kind of break is exactly what he needs. Too much at stake, and after proper breakdown, there might not be a way back.