We have a quite the serious Constitutional quagmire here. 20th Amendment states that:

and the terms of Senators and Representatives [shall end] at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin [...]

Riddle me this....

How are purported House members-elect lawfully participating in House business (election of a Speaker), if they are not actually members of the House until they are sworn in, which according to House rules, cannot happen until the election of a Speaker?

Sounds like the Constitution is long overdue for an amendment to clarify this glaring oversight by the Framers.

Furthermore, if our House has been functioning in such a disfunctional, arguably unconstitutional manner, seemingly since the beginning, have we ever truly had a legitimate Congress?

Time for a new Convention of the States to settle some of these big issues.