Without a DOJ, I don’t see much happening
It will take tougher Republicans than we're accustomed to, but there are options...
Mark Levin points out almost all these stonewalling executive branch folks, including even most of the Cabinet officers, aren't created by the Constitution, but by Congress. There was no DOJ until Pres. Grant! Before it was created Congress could and did enforce compliance without the executive. And can do so again. Then he reminds us how. It would take GOP spines and cajones, but, as he points out, can anyone doubt today's other side would fail to do it if the circumstances were reversed? If one isn't familiar with Congress's inherent contempt power this is a good 12 minute review.
The one thing I'd add, although I lack Levin's legal history background to confirm it, is that IIRC that power derives from being a legislature of a sovereign country. British Parliament had similar powers. As each state is officially sovereign over its own affairs I'd think each state's legislature should have the same powers. Obviously they should research the powers before trying to use them, but this means the the AZ Senate, now holding hearings on the last election, and being blockaded by a solid front of state office election thieves, should have the same kind of powers to lock up the stonewallers, or at least most of them, without any assistance from the crooks.
If AZ judges continue to block justice that may be the only way to rescue the state. It might be tough on the citizen legislators, but then ask the members of the Continental Congress how tough it was to fight King George! They should pray for the courts to come through as the facts are all on Lake, et al's side. But if they honor their oaths to AZ they should be quietly researching options like Levin outlines. If they become convinced their opponents have literally stolen the AZ executive branch, including the opportunity for any redress via the legal system, from the People, the People's branch must take whatever action it can in response. It's either that or admit to abdicating any claim to power at all and thus any claim to the state being a representative republic. Which the US Constitution says is a sufficient reason for SCOTUS to back them.