Is there an average cost per hour to hire a HIMS AME to take a difficult class 3 medical case?
I know the total hours will vary on a case by case basis.
By difficult, I'm talking history of anxiety,depression and ADHD.
I can't comment on your anxiety, depression, and ADHD, but I can compare it to substance dependence.
The responsibilities and complexities of HIMS are demanding on airmen as well as AMEs. I don't see any way a doc could do justice to the job part-time. A good HIMS AME will be upfront about this, and their advocacy efforts are invaluable to making a painfully slow process tolerable. Find someone who's full time work is as a HIMS AME. These doctors may cost a few bucks more, but they're worth it.
I haven't seen costs billed per hour. My experience has been that they bill per visit. It's not out of the realm to see $150-$250 per 1-3hr visit. It would be entirely justified for them to bill for their time advocating and coordinating with the FAA on your behalf, and I would expect the rate to be similar to their per visit hourly rate.
The AME is usually the smallest portion of the total HIMS expense. The real money kicks in to see specialists for evaluation. To give you an idea, the "full" neuropsychological battery can easily run $3500 depending on where you get it administered. Add a psychiatrist, requests to past providers, substance monitoring, non HIMS specialist visits, lab work, costs to obtain past medical documentation, ongoing SI compliance, time off work, travel etc. It can get expensive fast.
A reasonably straight forward alcohol dependence case can easily run more than $15k before a medical is issued. After issuance, SI compliance can run in the $1-$2k per year range for monitoring, psychiatric follow up, and medical exams.