Sundays are boring, so...
The following is an analysis of what would happen if the partisan makeup of each state's congressional delegation was determined based off of each party's overall electoral performance in each state's 2014 House elections.
Basically, I gathered the overall House vote for each state in 2014 (all the districts combined) and calculated how these percentages related to the actual percentage of districts in each state controlled by each party. For example, while Alabama Republicans only got 65% of their state's House vote overall in 2014, they got 86% of the seats (six out of seven).
These discrepancies were then modified so each party received as accurate a number of seats as possible (Alabama Republicans now only received five seats and so on so forth).
The following is the data gathered. The first couple of colored columns represents the overall popular vote percentage in each state received by each party during the 2014 elections, the second group represents how many seats each party won, and the third group represents how many seats each party
should have won under the proposed system. The last column represents the overall partisan difference in each state's congressional delegation with the changes implemented. D_ represents Democratic pickups, R_ represents Republican pickups, and E represents no pickups for either party (in other words, a relatively more representative result).
As you can see, Texas was the only state in which third party candidates managed to get enough of the statewide popular vote to obtain seats - two for the Libertarians. I'm assuming (reluctantly) that each would caucus with the GOP, giving them a 234-201 majority. Hence, if the system was implemented starting with the 2014 elections, there would be no partisan caucusing difference between the 113th and 114th Congresses.
The following is a map of which states currently overrepresent Republicans and Democrats in their congressional delegations:
No big surprises there; red states give an advantage to red representatives and blue states give an advantage to blue representatives. California is the biggest offender, giving seven extra seats to the Democrats, while Texas, North Carolina, Pennsylvania, and New York each are off by three (only NY favors the Dems).
Here's where the fun starts. I've given disadvantaged state parties the appropriate number of new seats in each state based off of how many they deserve according to the above system. For example, in Florida, the Democrats are currently have three less seats than they should, so they got three new ones here. Seat flips are based off of which seats in each state the minority party got the highest percentage in against the majority party, so in Florida, for example, the Democrats got the three formerly GOP seats that their candidates got the highest 2014 percentages in.