Thank you for publishing an information discussion on the electoral college vs electing the POTUS via popular vote. While there is justifiable concern that Mr. Trump won the election in spite of Mrs. Clinton receiving significantly more popular votes it should be pointed out that Mr. Trump won 2,626 counties compared to Mrs. Clinton winning only 487 counties.
In my opinion it was the goal of the Founding Fathers that the POTUS have the widespread support of electors representing the various states. As you point out:
“a body of electors were to be chosen only at the time of election, only for the purpose of presidential selection, and only by “the great body of the people,” . . . the presidential selection could be made safely in the hands of competent, independent men.”
It was never intended that the POTUS was to be selected directly by the general population. The process has evolved so there are now presidential caucuses/primaries for each political party to select delegates to attend partisan national nominating conventions that select the party nominee to get listed on the ballot for the general election. The general population is limited to registered voters — as it should be — who are allowed to select from the available choices. Remember that voting for POTUS is not for the nominee but for his/her previously identified electors who are not listed on the ballot for brevity. The presidential electors of today are not the well respected, educated, principled individuals whose judgement could be trusted by the state citizens represented.
Not to belittle your mathematical analysis, but in my opinion your proposal of adding a fabricated 51 electoral votes to the popular plurality vote winner is just applying a fudge factor to increase the popular vote influence on the outcome. It would require a constitutional amendment of Article II, Section 1 that would probably be supported by highly populated states and opposed by lowly populated states.
You mention that Maine and Nebraska allocate the electoral vote which places more emphasis on the plurality vote. That’s a compromise between the popular vote and the current implementation of the Electoral College. In my opinion a more desirable alternative to your proposal would be to preserve the Electoral College as is — thus avoiding a constitutional amendment — but to change how the states allocate their electoral votes.
I think Maine’s 2020 implementation is the best approach. Ranked choice voting — instead of plurality voting — for the POTUS will mean that the winning candidate has received at least some support from a majority of the voters. Allocating the electoral votes — statewide winner receives 2 votes and congressional district winner receives one vote — is a reasonable distribution. I suspect many state legislatures would oppose it because they like maintaining power of one of the members of the political duopoly.