The election in the HoR happens 2 weeks before inauguration day, so the SoH isn’t acting President before that date, either.
Correct. But the process of the House and Senate could go forward, and maybe end this mess before you reach that 3rd week.
Bigger discussion item is idea that the Supreme Court might invalidate several state election results (not just Penn), and the House method of choosing the president suddenly becomes a big issue by the 13th of December as the EC situation can’t function because the Supremes cancelled their results.
My suspicion is that a minimum of ten states will be cited for serious fraud or simply bad practices in handling the election. In this case, I can’t see how the Supreme Court would allow the EC to function.