I think you're underestimating said bias toward two parties. Unless we switch to approval voting or the like, you'll never see a stable third party in this country. The simple math makes it so that given any three parties, the two most similar parties have the incentive to both back the same candidate, because the alternative of running opposing candidates invariably leads to those candidates splitting the vote and giving the election to the least similar party. And by the time they're both backing all the same candidates they might as well merge into one party.
The thing that can happen, and could achieve a significant improvement, is for a new party to come about that replaces one of the existing parties. That allows you to throw out the old leadership and start over with a clean slate.
The biggest difficulty is in building a stable coalition. If you want to eject the religious zealots and the climate change "skeptics" and the imbeciles who want to keep government out of Medicare then you need to replace them with something that supplies an equivalent number of votes and/or campaign funding.
Tech is a good start, but it might not be enough on its own. But the nice thing is that once you've decided who you're not going to invite into the tent, you know exactly whose ox to gore. I have to imagine a fiscally conservative-leaning party would have a lot easier time capturing the votes of centrist Democrats if they were pro-choice, pro-science, pro-education, pro-alternative energy, etc.