IVF coverage denied for Z31.83 diagnosis code

My wife and I have been seeking IVF treatment and this year coverage was added to my benefits for infertility treatment (up to $25,000) but our insurer keeps denying it due to an exclusion of Z31.83 diagnosis code.  The insurer does cover the various IVF CPT codes but the one diagnosis code associated with the treatment they won't cover and therefore refuse to cover infertility treatments.
 
My wife has stage 4 endometriosis and hydrosalpinx.  She had surgery to have her tubes repaired/drained but the damage was so great that the surgeon could only remove one tube as he "couldn't discern her anatomy." We subsequently went to a specialist in another state who performed robotic-assisted surgery to remove her other tube and "clean up" her lower abdomen due to significant adhesions and remove endometrioid cysts. 

On one hand, the fertility clinic says Z31.83 is the only diagnosis code that can be used for the actual treatment (i.e., embryo transfer), however the insurer won't cover it and is telling the clinic to use another diagnostic code.