Well it's a time vs "not a whole lot of difference in cost" sort of deal.
Insurance service psychiatrists have nothing to bill for in an "evaluation " so they decline to do them.
Civilian Forensic psychiatrists use DSM 5 and that may be uselss to the FAA and cost about $3K. Now, if you can present evidence (like a 15 year pharmacy printout) that you have had that one and only episode of anxiety disorder and nothing preceding it (ONCE only in your lifetime) the CAREFUL history of a forensic psychiatrist WOULD be useful to the FAA even if DSM5 (History is history, period).
The HIMS psychiatrist runs about $3,500 usually and he will know how to summarize his report per part 67.
So the answer is, "Maybe".
But the HIMS psychiatrist in Phoenix is VERY VERY excellent (Name starts with an "L"). There is a reason she has a line at her door.