Statewide multimember districts elected by party list with more total seats (500 would make sense) would eliminate the problem entirely and break the two party system for good, but fat fucking chance of that happening.
Wouldn't that require ranked choice or instant runoff voting or something? It's probably more likely that the two party/FPTP system will be slowly chipped away until it reaches a point that it changes over rather than a massive outright all-at-once reform.
edit: How would that deal with the tiny states vs big states like California, Texas, or New York or large area but low density states like Alaska (though that's an extreme example, it's population is actually similar to the Dakotas or Vermont). 10 might not be enough for a big state like Texas or California, but it'd be rather over-represented for small states like RI or Mass.
The US congressional elections have three major issues: single-member districts, election by plurality, and massive population size per district. The single-member districts mean that each district only elects one seat, plurality means that the individual candidate with the most votes is elected (FPTP).
Single-member FPTP districts result in a large number of wasted votes. The crux of the issue is that the system doesn't distinguish between winning by a landslide and winning by a thin margin; 51%/49% is identical to 85%/15%. The losing 49% in the first case got absolutely nothing, while the bulk of the winning 85% had their strong winning majority wasted by being confined to only their own district (along with the 15% of losers who also got absolutely nothing).
Even if the national vote totals end up roughly matching the representation (which they don't), it hides the vast number of wasted votes canceling each other out in this ridiculous great game of outside money influencing what should be local elections. Incumbents in safe districts barely bother to campaign (and often even run literally unopposed), while millions of dollars originating from national party and PAC funds are spent bombarding the people who happen to live in a district that might flip.
The only problem that ranked voting addresses here is the spoiler effect, as well as randomly getting the odd independent in office (often by accident on the part of the voters). I remember mainiac saying a while ago that ranked choice in Maine was pretty pointless, and I disagreed; I think he's right now, it really isn't enough.