A Tale of Inefficiency: Today's Math Problem

Names were removed from this post because the writer is still in shock of the vast inefficiency described.

There once were 2 pain specialists in a town.
There once were ONLY 2 pain specialists in a town, at least ones with MDs.
There once were no other choices for patients to visit in said town.

Pain specialist #1 takes 3 weeks to get you in the computer system, then 2 more weeks to make you wait for your appointment.

Pain specialist #2 doesn't get your referral...because they require it to be faxed...and they are closed on Fridays...and the fax machine fills up and stops accepting information...and doesn't tell the sender that their information wasn't accepted.
Pain specialist #2 also sends you to voice mail when you call to ask specifically if they received your referral...then doesn't return your phone call.

Patient X really doesn't like either pain specialist option right now but surgeon Y will not consider patient X's pain to be adhesions until pain specialist #1 or #2 rules out nerve pain as an option.

Now patient X knows that 2 different nerve pills and a nerve cream made no difference to the pain and is highly skeptical that pain specialist #1 or #2 can actually help (especially since pain specialist #2 never even received her referral).  Yet patient X also knows she will have to go through the appointment and pay her insurance's specialist copay regardless of said pain specialist's ability to help if she wants surgeon Y to consider adhesions as an option.

Using the information given as well as your own personal experience, how many days will it take for patient X to finally be given a diagnosis and for a doctor to be willing to act on it?
(Remember your answer must take into account only working business days and time off for holidays, as well as golf excursions for the doctor.  We wouldn't want them to miss out on those.)