It should not drive you nuts that the two-party system is the best we have. The two-party system is the natural mathematical consequence of our electoral system, "divide the land into districts and each district holds a first-past-the-post vote." Fixed-point theorems are sufficiently robust and human intellectual attitudes sufficiently squishy that we will always be coerced into this. Abstract mathematics literally caused the US civil war, and it will keep amping up the anger and mistrust and divisiveness over and over, again and again, because the fixed point of our electoral system is two parties who both say "you're either with Us or Them, you have to choose."

[I have seen a recent push of progressive voices against gerrymandering, including both political sides (e.g. Schwarzenegger on the right and John Oliver on the left)... It is important to understand that the elimination of gerrymandering would help make the parties a little more volatile and would thereby help things get done, but it is very much a "rearranging the deck chairs on the Titanic" measure, the polarization and 50/50 split would stay there even if you used mathematical methods to do redistricting.]

We have a fine proportional system that we use to allocate our Representatives to the States, and it is worth remembering explicitly that the House was created to solve one big problem: we have a bicameral legislature because the Founding Fathers were split between people who said "every person should have an equal say in terms of what laws are passed" (House) and "every state should have an equal say in terms of what laws are passed" (Senate). People from low-population states did not want city-folk running over them, and that is what the Senate guarantees.

What we need is to use this same proportional system to allocate our House Representatives to the various national Parties. The founding fathers did not want to think in terms of political parties because they were all big intelligentsia egos who figured that you'd want to really know who you were voting for. What they didn't consider is that in a fork-o-philic model, someone can basically just make their own party about their personality and they'll get one or more seats if they're influential enough. (A great example is Trump's analogue in the Netherlands, a man named Geert Wilders, who basically just made a party that was about him and his own isolationist nationalism and it has been remarkably successful as the Netherlands has similar pressures to those that got Trump elected.)

No more gerrymandering, no more 50/50 partisan split: for the House, everyone gets an equal vote for a party, and the parties get proportional representation in the House via their Webster allocation of delegates. While the party composition starts off Republican vs. Democrat, in short order the Freedom Caucus and Green Party and Libertarians and so on will have their own representation there, too. The 50/50 split in the Senate will probably still infect the House, and your parties in the House will consistently be "left-ish" and "right-ish", but the openly nonpartisan House politics will also feed back into the Senate and kill some major road-blocks.