In the end, though, if a majority of the House met, elected a speaker pro tempore and so on, there’d probably be nothing anyone could do about it.

He could presumably even do it after the resolution removing him is adopted and before the motion to reconsider is tabled:

A member can say anything they want on the floor by putting it in a resolution and giving notice of their intent to offer it as a question of privilege (even if they do not then actually offer the resolution, or even if the chair rules that it does not qualify as a question of privilege).

It happened literally today.

❓
A bizarre claim. Obviously not true.

This is not a trivial issue. Here’s an instance in which a member spectacularly failed to have another member censured, because he tried to do it with a ‘motion’:
www.youtube.com/watch?v=PBLB...

In those days the Rules Committee didn’t stuff so much junk into each rule.

*of the final session of a Congress*

An adjournment sine die between the first and second sessions is not enough.

That would not be enough, because nowadays the clerk of the House and secretary of the Senate can receive veto messages during adjournments. The only time a pocket veto is possible is after the adjournment sine die of the final session of a Congress.

The resolution has to allege that there has been an unreasonable delay.

If he does nothing with the bill, it just becomes law.

The good news is that at that point, a member could offer (as a question of privilege) a resolution dealing with the matter – no need for another discharge petition.

They put Mr. Bean in the chair immediately before him, I guess to make Moore look less bad in comparison.

Seriously: My concern was that it might constitute a change in the rules of the House. Upon reflection, though, given that (as we saw today!) a resolution removing a member from a select cmte (also appointed by the speaker, not elected by the House) is a QoP, I think this would probably qualify too.