I'm trying to picture in my mind the Venn diagram that can accurately convey the overlap between GOP factions that adds up to 217 while satisfying all of their internal, transitive, mutually exclusive criteria.

There might not be any.

Clearly, the caucus isn't willing (yet) to just vote for somebody - anybody - simply because they need somebody - anybody - to fill the chair. No, the person they pick still needs to be right, politically acceptable to them so that they can defend the vote on substance rather than the "eh, we had to pick someone."

It's an astounding collective action problem. There's no mechanism by which they can bind themselves to a collective vote within the caucus. No matter who wins the caucus vote, every member remains free to vote for whoever they want on the House floor. There's no institutional framework with the power to reward cooperation or punish defection from the will of the majority. So even though they all want a Speaker, there's no path for them to get 217 votes for any specific Speaker.

So this may go on for quite a while.