I'm really sorry to break it to you, but I don't know the answer. I'm a Golf Teaching Professional. I've only taken a handful of lessons from other coaches in my professional life. If you really wanted to find the best golf instructors, you would have to ask golfers who have taken lessons their opinions. Find out how they ended up performing relative to agreed upon goals with their coach(s). But there isn't a system for quantifying this. Maybe I should work on it:)
Best in State/Country Lists: The most popular lists choosing "The Best Golf Instructors" build by surveying Golf Instructors about other Golf Instructors. I've filled out these lists before. I may vote for a few people I've worked with before and I know some of their skills or coaches I see once in a while online and I think they sound fairly smart. But I feel really awkward casting these votes as I really am not in a position to judge their ability. It might make more sense to ask their students. My personal experience does allow me to say safely that most of the teachers on the "Best in State List" for Minnesota are pretty solid instructors. BUT, there are usually 1 or 2 that I know are mediocre to poor at helping people play better golf.
PGA Awards: Another measuring stick some people are aware of is the PGA's Best Instructor or Junior Instructor award. This list is decided upon by the board and committees of the local PGA Section. PGA Professionals who win this award have to fill out a lot of information and give a lot of background and references to be considered. Knowing that, you can be sure that a Teaching Pro who has won this award does have some merit behind what they do and, at a minimum, put time into their profession and are serious about it to put together a portfolio.
Find a Coach for YOU: Award winners from the lists above are some of the best instructors around, even with a few duds thrown in there. But whether they are on the list or not, you need to find an expert that is experienced in fixing your needs. Below are a few types of coaches you may have heard about or will find that may or may not be the right fit for you.