The Speaker of the House Problem Solution

Take whatever the number is — about five, I think — honorable House Republicans and add the entire Democratic caucus, thereby forming a majority of members of the House, and elect one of the honorable Republicans Speaker on his or her promise to carry out the functions of his office in a responsible, honorable, competent way. The vast majority of the other House Republicans would condemn, ostracize, and “primary” their “traitorous” colleagues, but the institution of Congress and American Democracy would be saved. The honorable Republicans would be hailed as heroes by all people of good will. Some might lose their Congressional seats in primary contests, but they would all have gained a lot more than they lost.
Question: Are there enough honorable Republicans in the House for this to happen?