"George Mason suggested in 1787 that the House of Representatives should elect the President to a single, non-repeatable term of seven years. It remains simple, and the advantages of the alternate system have evaporated as the population grew and power transferred from states to the national government. A modern solution might keep the President's four-year term, limited to one term, and require that the elected President not be a sitting member of the House."

George Mason's suggestion is preserved in the Constitution and invoke when the POTUS candidate does not receive a majority of the EC votes. The current EC method results in increasing sustained voter anger between the POTUS losing and winning party members. If the POTUS was elected by the House then the public anger would instead be directed toward House members. Maybe the public would stop reelecting the same representatives who fail to honor their campaign promises and their party platform. Your idea has merit and I will deliberate on it in the near future. I may incorporate a version of it in my list of grassroots election reform objectives.

"The problem of the Vice-president is solved because the House, now in session full-time, can replace the President quickly in need, so the President Pro Temp of the Senate need stand in for an incapacitated President only until the House can elect a new one."

I suspect this is an impractical implementation. I assume the Vice-POTUS is kept current on international issues that could immediately impact our safety and defense. Also, there are probably traditional duties performed by the Vice-POTUS for the duration of term in office. Its probably best that the POTUS and Vice-POTUS be members of the same party. Maybe both should be elected by the House.

There would be an enormous impact to election campaigning. House representatives would be inundated with voting requests from the public - citizens and lobbyists.