Hi there,
Sorry for your pain. Breakups hurt, no matter what the reason is for them.
Let me ask you this. If he weren't alcoholic, if he were just some musician dude you'd met and had been involved with for six years and he decided to call it quits, would you be considering begging him for another chance? I think sometimes we think it's "just" the alcohol problem, and if he would just straighten himself out, we could have this fantastic future together. But if you read around these forums, quitting drinking doesn't solve all the problems--in fact, it's often the beginning of a whole new world of uncertainty and pain.
My suggestion to you is that you accept this man's decision that he does not want to be in this relationship any longer, lick your wounds, feel crappy about being "dumped" for a while, and then work on picking yourself up and building an awesome new life for yourself. One that doesn't involve being chained to an anchor that's weighing you down. By your own accounts you have a lot going for you.
Hugs,