Possible middle ground if you can't immediately get what you're hoping for: Explain to the new Director that in the medium term you'd still like to be able to also work with the prior domain, and try to negotiate roughly "if I can fix this team to the point where it doesn't need me, then I get moved to cross-domain work."

This has obvious risks of them not coming through once you achieve the first part, but if this team is as screwed as you describe and management are confident in you being able to unfuck it - and of needing somebody at your level of competence to do so - then it might turn out to be a net positive route for you, your career, the team, and the company.

Also might be easier to sell to the new boss, and a deadline for them to actually deliver on that promise if you can get it made of "when said stock vests" would fit your being willing to leave then and their being aware you've passed the vesting deadline for a decent chunk of options will probably give you a stronger position from which to press them to deliver at that point.

(of course there's lots of details here you know and I don't and I'm still on my first pot of coffee, but hopefully the general shape of the idea provides some inspiration that fits the full situation)