Considering that the House has nothing to do with affirming electoral votes (that is the role of a once-in-four-years Special Joint Session), and since the action of that Joint Session was signed by the presiding officer, Richard Cheney of Wyoming, your ship has sailed.
I think the House action would initiate a Joint Session for purposes of reconsideration of the certification of the result of the Electoral College vote. And procedurally, it may fall out of bed in the process.
There is a fair amount of law in support of the proposition that ineligibility vitiates the process. I still don’t think Barack is the President; I have looked in a very cursory way at the amendments and I don’t see where you go otherwise. It looks to me as though Joe as duly elected Vice President, is acting President until some eligible person is chosen.