The latest news on this front comes from a really interesting article at Ballot Access News written by the widely-respected election expert and advocate for third party/independent ballot access Richard Winger:
The best election law bill in Congress is HB 3863, which Virginia Congressman Donald Beyer introduced on June 11, 2021. It would convert most U.S. House elections to the Single Transferable Vote system, and would create much larger U.S. House districts. If enacted, it would substantially ease the gerrymandering problem. Unfortunately, it has not gained any co-sponsors other than the original seven co-sponsors.
Millions of dollars are being spent by wealthy individuals to promote state initiatives to abolish partisan primaries and create top-four or top-five systems. It is unfortunate that those same individuals aren’t instead promoting HR 3863.
The original co-sponsors are Jamie Raskin of Maryland, Jim Cooper of Tennessee, Ro Khanna of California, Jim McGovern of Massachusetts, Scott Peters of California, Joe Neguse of Colorado, and Earl Blumenauer of Oregon. All are Democrats.