I don't think the Dems will break history to vote for a moderate Republican speaker, nor will Repubs be willing to nominate such a person.
However, the Dems might support a vote to change House Rules to give the current pro tempore speaker the full authority of the House Speakership until the next election. Except technically I don't think the pro-temp speaker can even bring such a vote to the floor under current house rules (even kicking Nancy out of her office could and perhaps should have been ignored by Nancy as outside of the pro-temp speaker's authority).
But on the other hand, House Rules are simply whatever the majority of the House decides that they are...
wouldn't that violate the constitution? If they "chose" to give temporary athuhority to the temporary speaker, and not actually chosing a nominated speaker, they are directly violating the language of the consitution that directs them to chose a speaker of the house by a vote of the majority. By doing such a thing, they are basically side stepping what the constitution says they must do.
Section 3:
Article I, section 2 of the Constitution directs that the House
choose its Speaker and other officers. The Speaker is the only House
officer who traditionally has been chosen from the sitting membership
of the House. Manual Sec. 26. The Constitution does not limit his
selection from among that class, but the practice has been followed
invariably. The Speaker's term of office thus expires at the end of
his term of office as a Member, whereas the other House officers
continue in office ``until their successors are chosen and
qualified.'' Rule II clause 1; 1 Hinds Sec. 187.