Depending on where you are, there are boards certifying professionals. However, much would depend on the doc's track record and if he has a history of problems elsewhere. You could also contact Invisalign, since they have a certification program.
Your example does show the importance of checking out a doc in advance. I had a similar experience about 20 years ago where a family dentist wanted to correct my deep bite with regular braces. I let him do it based on the fact he had taken over the practice and was recommended by my retiring dentist. As he progressed with work on my teeth, I realized he had very limited ortho experience and really should not have been doing this work. However, in my case things did turn out better - I didn't have a serious relapse for a number of years. I did, as you said you are going to do, changes dentists after I realized this doc was trying to do other high priced services deemed unneccesary by second opinions after he had completed my ortho work.
For anyone with special problems, I think an orthodontist is best as they can decide the best treatment method and follow up with other methods should one fail.