Father in law saves the day
Well, my father in law came over for dinner and I was able to talk him in to having a look.
He pulled the handle off the shower and the back plate to look for a leak there. Nothing.
He pulled the drain cap off and found that there was no caulk around the area where the drain sits in the base of the shower. So, I caulked in that area and two weeks later no leak.
His suspicion is that the water was getting under the drain into the base and then wicking up via a stud or something and getting the green board wet from behind.
Anyway, I don't have to replace the shower!!