Easy way to book this: tournament to crown new champion.
Out of the box suggestion I saw on Reddit: have MJF cash in the chip on Punk. Punk is medically unfit to wrestle which leads MJF to demand his forfeit. AEW rejects it and it leads to MJF throwing a massive bitch fit, threatening to make it a legal matter and/or threatens to leave again.
MJF is getting is ducks in a row in the meantime, tournament commences with Hangman winning it with MJF also revealing his legal challenge was successful. Hangman has belt taken away and MJF is crowned world champion in a sleazy, dirty, most MJF way possible. Hangman v MJF while you figure out the rest down the road.