I found a fitter that has done work with a good local randonneur albeit one who rides very aggressively at the front of the pack on a road bike with a more race oriented position. I'm a bars at or slightly below the saddle guy who is going to be middle to back of the ride in terms of speed.
I think you have the right understanding as to what a bike fitter can accomplish. Checking the reputation of a bike fitter is key. Also, inquire as to how long the appointment will last and what is involved. The bike fitter should measure your build, use specialized equipment to replicate the ideal geometry, use video and a power meter to check your performance, etc. The process of fitting a bike usually starts at the feet with the correct installation of cleats, then the seat is set for both distance above the pedals and fore-aft location. Once the cleats and seat are positioned, the reach is adjusted.
I explained to my fitter that I was looking for long distance comfort, first; hill climbing power, second; and aero efficacy third.
The bike is very comfortable;
Bike fitters are not miracle workers nor are they all charlatans and thieves. It should take very little diligence to weed out the pretenders. I do not consider a good bike fit to be a DIY project, just as I would not want to tailor my own suit.
Michael