To fix the Parties, you repeal the 17th Amendment and get the Presidential electors chosen by the state legislatures.
You also amend the Constitution to limit the Federal Government's powers.
That would change the balance of power between federal and state governments, but it would do virtually nothing to change the Republicrat duopoly.
To fix the party issue (by that I mean the game theoretic stability of the two party state) there are a few things to be done:
At the Presidential level:
Federalize the Presidential nomination process, so that the Dems and Repubs don't have 50 venues to scuttle third party candidates with nuisance lawsuits. If a citizen's vote is held for President, have a nationally uniform Presidential ballot on election day (no comment here on the EC). On election day you get a Presidential ballot, and a ballot for everything else. (Ironically I've heard people make the argument that having states determine the federal election process reduces the likelihood and impact of systemic problems on Presidential elections, when it obviously makes problems 50 times more likely. It only takes one state with a bad ballot design to mar an entire election.)
For Congress (and states):
Abolish gerrymandering either by abolishing Congressional districts altogether and going to statewide elections by party. (Yes, that would institutionalize the parties, but it would instantly mean third, fourth, and fifth parties would get representatives.) If districts are to be kept, mandate that all district boundaries to have a strictly limited aspect ratio M:m, (where M= maximum distance between two points in the district, and m= minimum length of a line segment bisecting the area of the district), and be convex, except for no more than (say) 10% of the area AND (say) 20% of the population - the boundary of the non convex portion determined only by rivers (of a minimum width) or county lines. Also end seniority in determining committee positions. Committee positions are assigned by random drawing, but can be traded.
For all politicians:
Public servants are performing public acts when discharging their duties. As such, there is no right to privacy when on the job, as their entire job is public. Mandate full time published surveillance of all elected federal officials while at work or conducting government business (mandate it at the state level for state elected officials too), and make it a felony for an elected official or public employee with direct regular access to elected officials to discuss policy with private citizens without published surveillance. (Grant exceptions for legal privilege, protected privacy, and security issues - but worded carefully so that military industrialists can't sneak general business in under security issues.)