Sorry to take a less positive tone. But you asked for input.
Very few alcoholics, from my experience, will change their behavior based such a loving letter. They are in denial, which is not a river in Africa. It is the complete delusional state of mind alcoholics live in.
You sound like many of us. Unfortunately, you can not be reasonable with unreasonable people. And alcoholics are unreasonable if anything.
Winning any war, be it love or conquering nations, is a process of planning for and winning small battles along the way. I suggest you prepare yourself for the next battle. What to do after this letter doesn't have the desired effect? If you come up with a plan, and the letter works beyond you wildest expectations, then you've only lost a little planning time and the rest of your life is lived happily ever after. However, if you wait until you realize the letter produced zero net change to start thinking about what to do next, you will be very far behind.
There is plenty of good advice, based on hundreds of years of collective experience, here on this forum. Take a read through a couple hours worth of posts and see if some paths might become clear.
If you do, you'll see a re-occurring theme from me. And that is to not waste another minute trying to change an alcoholic. I've been trying for years, and wish I hadn't. 20+ years later, I'm left with fewer friends, less money, and a lot more baggage for myself. If I knew then what I know now, I would have packed my bags at the 2nd sign. The first one would have compelled me to put her on notice, and the 2nd time I would have been gone.
Or you can try to change your alcoholic. It might work. Probably won't. Once you get a decade or two together it becomes much harder to leave. you can put your best effort in now, with clearly defined time based goals and see how it works.
good luck.