One main reason Reince Priebus started pushing for this is that this plan would have helped Romney in 2012. Kevin even says so in his post: that it would "put a dent in the DNC's perpetual 56 EV head-start every quadrennium".
Political victories should not play any role in reforming the Electoral College. We may control many state legislatures right now, but we will not forever. And if we lose too many legislatures, adopting this plan would screw us over for 2 or 3 elections, depending on which decade we're talking about.
If we are going to reform the College, it should simply be eliminated. It has lost most of its purpose. It was created in an era where the Framers expected this country to not have political parties. Parties have become a toxic force in American politics, and it is one of the reasons that the College has become irrelevant. The other reason it was created was because the public was not as informed about candidates as they are today (of course, it was impossible to be as informed as we can today; not to say that today's voters (especially university students) are often that informed, but they could be if they wanted to be).
Kevin, you say "What did the people's voice really say in the 57th quadrennial presidential election? And in order to figure that out, we need to know what the Electoral College map would have looked like if every state ≥ 4 EV used the Congressional District Method for allocating their electoral representation."
The people's voice really said that they wanted Barack Obama reelected. It is sad; but it is true.
Looking at what the College map would look like if we used CDM just tells you who gerrymandered better. And that answer is easy: our party, the GOP. Yes, the Democrats did it in Illinois, but we control many more state legislatures, and it is quite obvious that without some tricky maneuvering (even here in Michigan), the Democrats would have a lot more seats in the House.
Changing the College for temporary political gain is dangerous, and if the Republicans do this, give it time, but we'll be quoting Mr. Gump in a few years... "Bit me right in the buttocks!"