Thank you folks for your comforting words. I know I am doing the right thing for Jack, and it's only natural I'm going to do my best for him to get him better. I will not let him go from me until I have exhausted all options, I just wouldn't. Naturally if he was in pain or in any kind of stress that I couldn't stand to see him in I would let him go. But he honestly isn't. He's been lying on the sofa asleep next to me, and I've been smoothing him, he's purring away, apart from breathing very shallow and a bit fast.
I will give him more of his tablet with some tuna later on. I really do think I am on the right track, I know I'm not a vet, but I know Jack and have been as careful and tried to find out as much about hyperthyroidism as soon as I knew he had it, so I would be able to take care of him the best I could. I feel I am doing that, by trying to find other options.
I really do believe he needs a course of these or similar medication to take his heart rate back down again to normal levels.
I'm not just going to put him to sleep until I know I have done everything I could possibly do for him.

Thanks for your prayes, and please pray as hard as you can for him