What is this flaw in the Constitution that allows Republicans to maintain an unfair advantage? Well, here is the text, from Article 2, section 1:
"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"
The problem is that representatives are apportioned according to population, while Senators are not; resulting in, for example, every person who votes in Wyoming having 69 times the power of everyone who votes in California; a gross injustice.
Here is my proposal: An amendment be passed that limits the quantity of electors to the number of representatives, by simply eliminating the words "Senators and." This will have the effect of moving the Presidential election process so it corresponds much more closely to the will of the population, without any major change in the Constitution.
Of course, Republicans will scream their heads off to stop this, because they benefit from the current law's unfairness, but I suspect it would be far easier to muster support for this elimination of two words from the Constitution, than to eliminate the electoral college altogether, and my proposal would have largely the same effect of moving to a popular vote for President.