We have to clear cap space to sign Hayward to begin with, and I would be willing to bet that a big who makes less than Crowder or Bradley is part of that process. Additionally, there are multiple vet bigs out there who will sign for the room exception.
On the trade front, as posted elsewhere, my official prediction is Crowder for Juan Hernangomez from Denver. I'm also hopeful we'll sign Zaza Pachulia. That part of the roster will fill out quickly once we have Hayward. (If we don't get him, we'll certainly see the return of Olynyk, and also probably a big with the room exception.)