I would be very careful with the Temeril since your pup is hypothyroid. I am not a fan of it, as my experience with it and my hound (non grey) was not good, but he was on thyroid meds as well plus had cancer that we didn't know about at the time. It does help some dogs, but I would not be afraid of talking to your vet about it again and asking if you should be seeing more improvements by now. I don't remember a lot of drinking ect, but our dog would let himself out. The biggest for us was the behavioral changes, which were not a good thing. I do remember the first week of the Temeril was the first time he had slept through the night without itching and waking us both up, so I do remember he had fairly immediate relief. Some of the itching and scratching is a behavior thing after awhile, so if your grey has been scratching for awhile this may be the case. It is really important with the prednisone not to stop the drug cold turkey because that can cause problems too.
It is a very difficult thing, treating allergies-and sometimes you go with what ever works. Have you started with an elimination diet to see if he has any food allergies? One thing that would help Hogan was bathing, but I always used warm water on the cool side, as too warm water and too much soap can cause dry itchies as well. Usually he would hop in the shower and wait if he was really itchy. I only used soap once a week or so.
I hope Barney feels better soon.