...is to repeal or, preferably, amend a 105-year-old law that didn't directly affect the Electoral College.
That law is the Apportionment Act of 1911, which capped the United States House of Representatives at 435 seats. I wouldn't be surprised if most people thought that number was set in the Constitution. Well, it isn't.
How would this fix the Electoral College? See Article II of the Constitution:
Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.
The Electoral College is capped at 538 because the House is capped at 435. Amend the Apportionment Act to set a higher total number of House seats and not only does the House become more representative, so does the Electoral College.
Any other adjustment to the Electoral College would require a constitutional amendment. This one can be done by the 115th Congress and signed into law by President Trump.
If, that is, those butthurt over the outcome of the 2016 presidential election are really upset over the un-small-D-democratic outcome, and not just the un-capital-D-Democratic outcome. Call it an integrity test.