Advisor on medical leave only a few weeks before dissertation defense
Something (somewhat) similar happened to a friend of mine. The key to her solution was to get another chair while at the same time allowing her advisor to "save face" in the department. Basically she made it a matter of logistics (rather than irresponsibility or personality). 

She approached another (full professor) member of her committee to act as an ally. Then she copied the ally on a friendly email to her chair suggesting that the ally had "volunteered" to be a "co-chair" for the logistical purposes of the defense/graduate school paperwork. She explained that of course she wanted to keep her original advisor as the chair, but that the work start date seemed like it was making that arrangement impossible. She and her ally were able to arrange it so the original, medically unavailable chair would still get credit internally for having her as a student and would remain on the committee (as a "distance"/Skype examiner). 

I have found that, in general, difficult professors respond to subtle pressure from their peers (never their students) and prefer solutions where they can save face!