I don't think this is an inherently solvable problem in a deep sense in any foreseeable timeframe.

If a third party is to objectively determine whether rape has occurred, they would need both to have solid evidence of physical acts taking place and also solid evidence of absence of consent. This is tough in a situation which tends by its nature to happen in private (as do the corresponding consensual acts), and where consent when given is often implicit, and when not is often not made blatantly obvious due (c.f. "freezing up"), and where a variety of intermediates are possible ("I didn't feel that I could say no, but I didn't say no").

So this leaves us in a rather dismal post-modernist position of having easy access to rape-claims (c.f. truth-claims), but no easy access to anything beyond that.

There are a few things that could, conceptually, be done about this. For instance, we could have a society-wide safe-word that everyone would agree is to be used exclusively to mean "I do not consent to a sexual encounter"; and then we could have everyone's electronic devices constantly listening for uses of that word. This would come pretty close to giving us an objective readout for consent. And we already have decent forensic methods that can determine a fair bit about what's happened physically. However, having everyone's devices snooping on them all the time seems awfully prone to abuse, and there will still be many cases where victims claim they could not use the safe-word e.g. out of fear for their own safety.

Absent that, there are a variety of partial measures that one can take absent revamping all of society.

Firstly, we can recognize that rape-claims are better indicators of rape than our institutions seem to believe.

Secondly, we can make the process of reporting rape less dehumanizing than it currently is.

Thirdly, we can recognize that even though it is difficult to go from a rape-claim to better objective evidence, it's not impossible and we should try in more cases than we do.

This would probably have a moderate impact.

Simply being far more reckless with false convictions is probably not a good idea, as in addition to the impact on people falsely convicted, I think it is likely to greatly increase the MGTOW phenomenon (hardly a good thing for society) and make dating and romance a good deal harder for everyone by infusing extra levels of fear and suspicion (also hardly a good thing). There will always be errors with any process, and maybe we are a little too conservative with this one, but I don't think there is a great deal of leeway here without creating a nearly unlivable society.

Changing culture seems like it ought to work--there are differences of factors of ten or so across cultures--but right now the culture in the United States is not likely to be very amenable to change. I don't think you could even get Democrats to change because of multiculturalism--at the very least it would be a huge internal battle. And Republicans are a lost cause from the outset, except when it comes to giving out longer sentences to people convicted of something really heinous.

So prospects seem pretty dismal to me on a societal level for a really robust solution. For a factor of two or so, I think we have a good chance--and it's very important to try. But that won't change all that much qualitatively.