Payton. Mean people suck.
I'm unclear though on getting the fake review removed... if you are pretty certain who it is, then why can't you talk to the owner/admin & tell them the name behind their handle... surely when this reviewer registered as a site member, he likely gave the same name he books appts with. If all they are concerned about is proving who wrote this bad review (before they consider removing it) & the name you have for this person matches the name of the registered member, then you've at least pin-pointed who you think wrote it. Then they could contact him to investigate. Now if he's guilty, he likely won't even respond, & this may be all the proof they require for resolution. Personally, I wouldn't let this rest until it's deleted. I have recently experienced the fake review myself, & though it was a great review, it was fake, so it had to go. Many Hobbyists rely substantially upon the reported testimonials of our reviews as a research tool. Results to these situations however, are time consuming, but a false, negative review could hurt business, so you may consider pursuing this to the end, IMO.
It's ludicrous what some will do to harm others. A number of guys threatening bad reviews based upon the inability to schedule with you, may simply suggest looking for a different place to advertise. There are a few sites I refuse to post on, b/c the quality of those who would contact me were below the level I was seeking and/or I was being contacted by non-serious inquirers. Changing my advertising venues & requesting contact via Email only (while not answering unknown numbers on my phone), eliminated virtually all undesirables, functioning as a great filter. Worth a try...
There are no known review sites for reviewing Hobbyists, though there has occasionally been talk of creating one, & have even considered this myself, but I too can't seem to figure out a system that would be effective. And though I hate to admit, I think it would deem excessive abuse from Providers with their own issues, & result in dishonesty or disaster. I support my fellow-Providers & all, but I have seen some ugliness by unfair ruling.
What we DO have in our defense is a Providers Only section within many of our review boards. We also have blacklist sites to report the abusive guys (this is abuse), & I personally feel obligated to do so when I come across someone who's a jerk, b/c the whole idea is to reduce their chances of repeat offense through a long list of Providers, which supports a strong, safe community. So at the very least sweetie, you could document these circumstances within the appropriate sites so other Providers can take part in boycotting these losers. PM me for a list if you're unfamiliar with these sites.
As a last resort, provided your screening tactics are effective & implemented, I would remind these imbeciles that they have just as much at stake as you do, if not more. Defamation of character in return would not go over too well in their own lives, guaranteed.
Best wishes on resolving this!