I really hate to sound unsympathetic and/or discouraging, but I'm surprised you've been able to find so many alternative GPs at all. When I first started exploring the option of going in to therapy I needed to find an alternative GP who was part of some kind of scheme that aloud patients to get discount therapy. But virtually every GP clinic I phoned was refusing to take new patients - they were all too busy.
That being said, long story short I eventually had to get my regular GP involved in my therapy situation. In fact, he was really the only GP I ever dealt with regarding therapy, ect. I wouldn't say that he was either sympathetic or unsympathetic, but more like he knew his role in the process and performed it as kindly and un-judgementally as one could hope for. He was essentially reduced by the government to being a beaurocrat in the process. Medicare required certain documents to be filled out by him in order for me to see certain people and access certain discounts, so he'd fill that paperwork out for me without any muss or fuss.