Again, you are skipping the step where one House member and One Senator can object.
You are talking about the House process for electing the President IF the electoral votes are tossed out. You are jumping to the fourth quarter of a game without playing the first three quarters.
Pence starts opening sealed elector slates.
One Rep and one Senator object to a Judgement Pence makes.
They separate and debate IN THE Senate. There is NO house vote that occurs.
If the Senate cannot agree on enough slates to get to 270, the matter is sent to the House. That is the only time they they get to vote.
During the reading, they are mere witnesses who can object.
There is nothing you can point to ANYWHERE that says the House gets to vote on whether or not to send the election *to themselves*.
The Founders would have never constructed such an obvious conflict of interest.