To be fair:

The 12th Amendment depends on a couple of things here:

(A) the acceptance of the electors in the House and

(B) Pelosi actually authorizing a contingent election.

For what its worth, Pelosi can easily reject electors that she feels that are not legitimate. In fact, she can dispute every single elector if McConnell tries to play that game in the Senate (the electors are officially counted in a joint session of Congress).

Technically, there would be no tie in the electoral college of nobody accepts the electors. This actually swings the advantage back to the Democrats. There's no judicial standard that (a) requires Pelosi to accept electors, (b) requires Pelosi to hold a contingent election by January 20th.

(You did mention this as part of the Quorum, but I am just putting this all out there for those that may not have understood what you meant.)

Pelosi has to just simply stand her ground and, more or less, she will guarantee that Biden will be sworn in on January 20th.