The basic problem is that with a powerful, high profile person most people are afraid to say anything, figuring they can't fight the power. Hence the problem stays hidden for a long time and when someone finally comes forward then we get a flock of others joining in--and no way to be sure if the problem is real or jumping on the bandwagon for personal reasons.
Proposal: Allow sealed police reports. You can go to the cops and report a crime but indicate that you do not want to prosecute at this time. The police interview the person and gather any available forensic evidence that they can do so without talking to anyone else. The person filing the report indicates how many others must also file such reports before it becomes unsealed. The stuff goes into a offline cold storage system so it's basically immune from hackers--all that's on-line is the identity of the accused, the sort of crime, the ID of the cold storage file and how many entries are required to unseal it.
When a new report is filed the computer checks to see if it can find a set of files to activate. If not, it's simply accepted with no indication there are any other reports. If it finds enough it says so and notifies the other departments to activate their files also.
Now you have a set of reports that are generally going to be totally independent, people can't make up a story similar to what has been in the news. It becomes a much more solid case and it doesn't require anyone to be the first to stick their head out.
The basic problem with this idea is that the accused can claim they were denied "due process" if evidence is collected for a prosecution at some undetermined future date. The accusation is recorded, but the accused has no reason to preserved his/her own alibi or other records. If I had to account for my movements for the past six weeks, I could probably manage it. If I had to state where I was on this day 10 years ago, that would be another matter. This is why we have a statute of limitations for many crimes.
The real solution to this problem is to have prosecutors who take this kind of charge seriously, so a victim could have some faith in the system.