In my experience, coming off meds is always very difficult. The times I've had success is when I titrate down extremely slowly.
Your post caught my attention because I have also been having weird blood pressure spikes. I'm on two medications to lower my bp, but it's not dramatically lower. The doses are minimal, though.
The situation is very frustrating. It's great that your GP is arranging testing for you. So far, all my GP has done is change or add on medication.
Could the hormone increase your having indicate a thyroid problem?