I am so sorry that you lost your little Jack..... I know how much it hurts to lose a pet that you love. Also, don't ever think that having an animal that is suffering euthanized is "taking the easy way out".
When they are in constant pain, or have little to no quality of life, and no chance of getting well, it sometimes takes more courage to let them go, than it would to continue to care for them and treat them. No matter how much you love them, sometimes you have no choice. You have to love them enough to let them go.
I'm sure that your little Jack knew how much he was loved, or he would have never survived as long as he did, with a growth like that in his throat. Try to remember that he knew how much you loved him, and that you did all you could....no one can do any more than that. And know that he's now in a better place, where there's no more pain. Again, I am so sorry for your loss.