It's a reasonable approach- find an AME that also has a private practice. I
would also advise someone to ask around to see who is willing to go the
extra mile to help a pilot, and the FAA lists AME's who are also pilots.

Once you start getting into waiver submissions, extra tests and
documentation start piling up, so some docs may not be enthusiastic about
doing all of this for the $80.00 or so that they charge.

Others may not primarily be a family physician- one of our busiest AME's is
also a pathologist. It would be hard to rationalize a routine visit to see
him under some other pretense!

The physical exam for a class II or III medical is pretty superficial- the
medical history is more important in identifying potentially disqualifying
defects. (also true for general exams). Failing to list known problems has a
lot of implications in case of an accident or incident.

Still, a pilot AME may be more sympathetic and helpful. Most docs are
interested in helping people keep flying, not the converse.