I'm sure this has been said already, but I say go through with the plan, but maybe first try to convince coach Z to at least explain his long term plan and how cutting budget, ect. will help achieve that. But you can't force him to be reasonable, and if you need to, you are not only encouraged to but obligated to remove Coach Z from power, and the best way to do that is to go through the administration.
(Probably overkill, but Wikipedia agrees with me:
https://en.wikipedia.org/wiki/Right_of_revolution)
