For one thing there will be no Jan. 6 event in 2027. That's for the President and Vice president election.

The newly elected Congress people will be sworn in and take their seats on Jan. 3, 2027. Certificates of election are transmitted directly from the states to the clerks of the two chambers. I can't find any current procedure in the house or senate to challenge the validity of a certificate of election in Congress.

In the house, all members, even incumbents, are technically newly elected to a 2 year term. They must all vote for and elect a speaker before they can do anything else. The old Speaker and house leadership are not in office as of Jan. 3, 2027, so there is no role for them.

New rules require majority approval and a quorum.

Blocking democrats from reaching the chamber is not going to confer any legitimacy on the resulting proceedings. First, Congress was and still is fiercely protective of its speech and debate privilege from arrest. Doubtful you could get enough to go along with such an abrogation. Second, both chambers need at least half their members present to hold a quorum to do business. If they manage to arrest enough to deny a (rightful) majority, I recommend that democrats should also deny a quorum to underscore just how sham the sham proceedings are.

Finally, even if the above steps still fail, Constitutional amendments need 3/4 of state legislatures to agree after 2/3 of both chambers. Good luck with that.