I don't rate Gallant super highly, so I wouldn't mind missing him. He got a lot of praise for a very talented roster and chafed when Vegas ops offered any sort of feedback. I don't like that. DeBoer is a much better coach.
The Coyotes need a Bednar type. Someone who is tactically sound and is not wed to any ideas or styles (aka an up-and-comer with a history of minor league success). You find something that works best with the guys you've got. Someone flexible. Someone that won't be annoyed by having guys like BA and Stempniak (analytics liaison) chiming in. The HC should be the smartest guy in the room tactics wise but not so far up his own ass he can't listen to new information or ideas.
Van Ryn - Varady - Stillman is probably the perfect combo in terms of dollars vs output with all of that considered. Van Ryn did really well with Tucson and has credibility with the players. Varady isn't quite ready yet, and neither is Stillman.
Boudreau would be great for a HC - Associate situation with Varady, if he was open to it. But he'll probably hold out hope for a playoff team to come calling. Julien is an excellent coach but is too wed to his own ways and has a short shelf life. He'd also be great for a veteran group looking to get over the hump, like Sutter.
The Coyotes roster isn't atrocious like Detroit. There will be a lot of flexibility. They shouldn't have any trouble attracting someone eager to get a shot at HC.