You seem to be missing a key point: if the presidential election goes to the House, the vote in the House will be by state. Each state will get one vote. Here is what the 12th Amendment says.
But in choosing the President, the votes shall be taken by states, the representation from each state having one vote;
It doesn’t matter how many Democrat Representatives there are, what matters is which party has a majority in each state. I think you will agree it is hard to have an Electoral College tie where Republicans don’t also win a majority of Representatives in a majority of states.