There were multiple propositions for electing the President during the Constitutional Convention, but you should consider that the only body elected directly by the people was the House of Representatives until 1913 (17th Amendment). Direct elections were not something imbued innately into the writing of the Constitution - the value of direct democratic elections is something more modern, I think largely borne of the populist moment of the early 19th century. In fact, Alexander Hamilton writes in Federalist 68:

It was equally desirable, that the immediate election should be made by men most capable of analyzing the qualities adapted to the station, and acting under circumstances favorable to deliberation, and to a judicious combination of all the reasons and inducements which were proper to govern their choice. A small number of persons, selected by their fellow-citizens from the general mass, will be most likely to possess the information and discernment requisite to such complicated investigations.

So he isn't trusting of just anyone to make a judgement on who should be a president.

(The electoral college) will be much less apt to convulse the community with any extraordinary or violent movements, than the choice of ONE who was himself to be the final object of the public wishes. And as the electors, chosen in each State, are to assemble and vote in the State in which they are chosen, this detached and divided situation will expose them much less to heats and ferments, which might be communicated from them to the people, than if they were all to be convened at one time, in one place.

He states special concern over the general population sweeping (in current terminology) a meme into the Presidency. He also calls for special consideration to avoid 'cabal, intrigue, and corruption' and sees the Electoral College as a way to sidestep these conflicts of interest and vulnerability.

But the convention have guarded against all danger of this sort, with the most provident and judicious attention. They have not made the appointment of the President to depend on any preexisting bodies of men, who might be tampered with beforehand to prostitute their votes; but they have referred it in the first instance to an immediate act of the people of America, to be exerted in the choice of persons for the temporary and sole purpose of making the appointment.

To answer your questions

1. No, I don't read any need for a statistical tool here for the Electoral College specifically. There may be a better question regarding congressional apportionment here, though.

2. if you believe that Trump is a charlatan and unequipped to be president, then Hamilton would argue that the Electoral College was designed to keep people who have those traits from being President. He says:

Talents for low intrigue, and the little arts of popularity, may alone suffice to elevate a man to the first honors in a single State. but it will require other talents, and a different kind of merit, to establish him in the esteem and confidence of the whole Union, or of so considerable a portion of it as would be necessary to make him a successful candidate for the distinguished office of President of the United States.

However, I have absolutely no idea whether he viewed the electoral college as a system to dissuade harmful/corrupt decisions from happening in the first place, or one that could also be used to retro-act popular elections. I would love if someone could help answer that question.

source: Federalist 68