In theory you could have Congress mandate STV or open list representation for the House tomorrow if they wanted. Obviously it would become AV/IRV/PV/Whatever-You-Want-to-Call-It for states that have only one representative. Of course I find that less likely than Congress voting an assault weapons ban with bipartisan support on the same day.
To my understanding there are a lot more states than most people are aware of that do not use the one district-one representative formula. However to my knowledge all of those seats are elected at large with everyone able to cast as many votes as there are seats to be contested. There have also been several citywide attempts at PR. I believe that, at one time, Cincinnati and New York City both used STV as does a city just outside of Boston (Cambridge?) today.
I think the key is to have one of the various experiments with proportional representation here and there coincide with a city or state using multi-member districts and find that the idea becomes popular.
If memory serves, NYC adopted single transferable votes to prevent the regular Democratic sweeps of the city council. It worked and both parties were fairly represented for awhile and then it was abandoned because someone decided that a Communist might be elected.
If this fear-mongering didn't take hold and the city kept STV, I could see it having some chance of spreading statewide. In New York State the long standing convention has been to gerrymander the Senate for Republican control and to gerrymander the State Assembly for Democratic control. Those gerrymanders rarely fail. If the City's experiment with STV was allowed to continue, there is a chance that one party would use that has a way of ending the gerrymandering but allowing both parties a fair share of the power.* If New York manages to have proportional representation succeed, it could spread to other states. One state using it might be enough for it to become an alternative to majority-minority districts with nonsensical shapes spreading the concept even further.
*-New York seems to have a convention (in the British sense) that whenever redistricting is mandated the state will protect EVERY incumbent. For example, Long Island has five seats in the House of Representatives (4D, 1R) and nine seats in the State Senate (9R, 0D) with the party ratios rarely changing.