Oh, Toni, my heart hurts for you as I read this. It's so sad that the vet misrepresented Big Boy's prognosis (presumably for profit). I imagine that if the vet had been more honest with you, you would've made sure to be there for Big Boy. But you trusted Big Boy's doctor, and that is a natural response.
I adopted my cat from a shelter because she also seemed likely to be euthanized soon. The first vet who examined her after her adoption told me to take her right back to be put down, because he said it was unethical for the shelter to give a young 20-something (with no money) such a sickly cat. He doubted she would make it. But she lived for 16 years. The second time a doctor told me she was dying was just 2 weeks before the end; she had terminal cancer, and the diagnosis hit me like a ton of bricks. I couldn't reconcile the fact that, the first time a doctor told me she was about to die, I ignored him and nurtured her stubbornly and she lived a good long time, whereas now a doctor was telling me the same... and it was true. I also have regrets about her end, but what my loved ones told me that helped — and it certainly applies to you and Big Boy also — is that you gave this beloved cat SO many years that the cat was not "meant" to have. Your heart did that. I hope that Big Boy's doctors were able to make him comfortable in the end so that his final moments were peaceful.
You did what you believed was right, and you made the best choice you were capable of making at the time, with the intention to save him. Death leaves so many loose ends in our hearts; it's easy to blame ourselves for X and Y and Z in the aftermath. But I'm sure you were the perfect person for him, and he adored you until the end.
I don't know what your beliefs are, but if you do believe that there is more beyond this life, then I hope for you also that Big Boy is able to send you signs from time to time to make sure you know that there is no love lost, and you did not — not once — let him down.