The point to remember is that the Twelfth Amendment didn't anticipate the popular election of the presidential electors. When they wrote that language they considered it a simple task to deterimine appointments of electors from the state legislatures. The statutes do reflect that practice, but may violate VPOTUS's constitutional role. Traditionally VPOTUS's role is largely ceremonial, but we have never had this much fraud and contempt for the election laws of the legislatures before. VPOTUS can assert consitutional powers by refusing to recognize the legitimacy of slates of electors, and not even letting Congress consider them. Expect the Dems to run to Judge Sullivan in that case, and then it gets interesting because defenses of laches, mootness and standing won't apply to VPOTUS
Assuming for the sake of argument that you have interpreted the statute properly, you have completely ignored that by the Twelfth Amendment, VPOTUS presides and counts the votes. That implies the constitutional authority of VPOTUS to make decisions about the legitimacy of the certification of the votes.
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Here’s a recent report (updated December 8, 2020) from Congressional Research Service that reviews challenges to the validity of electoral votes.
https://fas.org/sgp/crs/misc/RL32717.pdf
Under §18, the President of the Senate is the presiding officer and his function is to preserve order, which encompasses the authority to decide questions of order. But at the same time the report notes that “the statute is not explicit on this point”.
My understanding is that tellers record and count the electoral votes. When this process has been completed, the presiding officer announces whether any candidates have received the required majority votes for President and Vice President.
Since both chambers consider any objections that are raised it doesn’t appear that Pence would be sole arbiter of the legitimacy of votes. But, on the other hand, Gore’s actions in 2001 (see page 5) are particularly interesting and would seem to give Pence some latitude to influence the counting process.