It turns out that the Electoral College, per se, is not what distorts the system so badly. It is the winner-takes-all method of allocating each state's electors. Can we break the winner-takes-all habit?
There is precedent. Decades ago, both parties allocated delegates to their national nominating conventions by winner-takes-all, until this blatant unfairness was challenged, then eliminated. So why not take the next step by dropping it from the process of choosing electors? Again, this would require no tinkering with the Constitution, though changing applicable state laws might entail a fight.