"Overall my best guess is that roughly half of all rape accusations are false and roughly a quarter of real rapes go unreported. "
Wubba wubba wubba!
That sounds like you talk to guys and not women. And yes, there are totally false rape accusations thrown around, although many don't get further than the cops asking a few questions. But somewhere between 5-10% of rapes get reported, and maybe half of those go on to be an actual investigation (ie pressed charges).
It is a real pain, and a waste of time all around, but any credible report of a sexual crime needs to be investigated. Most false complaints are solved after 5-10 hours of police investigative work is done on them. As in you case, a couple of interviews and it's sorted, reputation damage aside.
My personal experience is *every* woman over 25 I've known has either been raped, or something damned close. Most multiple times, often by the same attacker. About maybe 10% of the guys I've known have been accused of any sexual crime, and the ones who have raped people seem pretty unable to accept it. You know, that the drunk 15 year old totally wanted it etc. So I think your numbers are waaaay off.
For vindictive stuff, it's the family accusations of stuff against kids, since that isn't quick to disprove.
Since I image you'll be all "piffle, mens have it worse" just remember that about ten percent of victims of sexual assault are male, but you won't hear anything about them. Being falsely accused of rape will lose you some friends, admitting you where raped will lose your entire social circle. I'll take hate and anger over pity, at least you're a real person to other people.