That only controls the presidency. A significant progressive caucus could force presidents to the bargaining table.

Really its first past the post that is locking out 3rd parties.

Have you heard of abolishing it?

I am not sure how your electoral college works, as a non American, but I do know America had/has more than two parties. Why would the two give in to people's will if they believe they have a duopoly. Isn't trump's whole thing that the populists republicans basically voted him in favour of a more moderate conservative, basically changing the party from within.