First, the Motion to Vacate is just a rule, and those rules can be changed my a majority of the House - conveniently the same threshold that is needed to elect a Speaker. It is quite possible that a bipartisan coalition to elect a Speaker would also negotiate a change to the rules for the Motion, similar to what Pelosi did when she was Speaker, and wanted to make sure her thim majority could be effective.

Remember, as I said in my original post, there are some Democrats who would be either unwilling or unable to actually go along with all this without themselves committing political suicide. If, for example, you have 5 Democrats who can't go along with this, that means you now need 9 Republicans willing to put their own standing in the party at risk. The more Democrats that either can't or won't go through with it, the more Republicans you need, and therefore the less likely any of this is to actually happen.

Second, I am assuming that any hypothetical support of a moderate Republican by Democrats would not be in conflict with Democratic leadership or a challenge to their authority. On the contrary, it would be done with their blessing, extracting concessions from the new Speaker that the Democratic Leadership would find acceptable. And there are ways to hold that Speaker accountable that stop short of firing him.

And how do you go about doing that in any meaningful way that the GOP can't just shut down with a majority vote? How do you do that without threatening to oust that speaker and putting us right back in this position, only without a bipartisan coalition next time as Democrats say "see? I told you this wouldn't work."

Third, I am assuming that any coalition support would be done in favor of a Speaker who is actually interested in governing,

The ones who might be willing/able to do it while still being palatable to Democrats wouldn't want to be within 10 miles of that gavel right now. Notice how all the ones willing to step up to the plate are the ones that are just as bad or worse than McCarthy was.

So all they really need to fundamentally agree on is to not hold the government hostage every other vote.

And while we're at it, we can ask serial killers to just not kill people every other day. Heck, can't we just ask criminals to stop doing crime stuff? I'm sure doing so will be just as effective. These people are here specifically to hold the government hostage on every other vote. Why do you think no sane Republican (an oxymoron, I know) wants to go anywhere near that gavel right now? They'd be in the same position McCarthy was, if not worse.