One Possible Way Out
Anyone reading this knows what is happening there. One solution would be for some Representative who is a Republican to resign from that Party and declare to be an Independent and a candidate to be the new Speaker. That person could get all 212 votes of the Democrats in the House. Surely four Republicans — a candidate for Speaker can vote for oneself — could be persuaded to vote for that person, giving him or her the number of votes needed to become Speaker.
Obviously, that person would only come from a congressional district that voted for Joe Biden for President in 2020. She or he would definitely be putting getting re-elected at risk. There is also the chance, however, that in making that move that person could become an all-time political hero.