Quick update for anyone following this:
Heard from lawyer on Friday. He has drafted a consent order to send to ex's lawyer - I read it, okayed it, and asked him to send it out as soon as possible. The draft is really simple: basically, it says that ex and I have agreed that it is in Kid's best interests for me to have sole custody. Ex will have "reasonable and generous" visitation and will have the right to receive all information pertaining to Kid from schools, medical professionals, etc. If either party wishes to amend this order, they must give the other party ten days written notice before commencing court action.
There's no mention of alcohol or addiction anywhere. The lawyer says this is meant as an inducement to ex to sign. If he signs on consent, there's just this bland statement about how we have come to an agreement. If he doesn't sign and this goes before a judge in some form, I will need to prove my case which will involve bringing out all the evidence I've organized about ex's addiction and his issues with mental illness, most of which makes him look pretty bad (and crazy). So - signing on consent = he keeps some of his privacy. It's a mildly sleazy strategy (and plays on the addict's mania for secrecy), but I'll go for anything that will get his signature on a document for sole custody.
Now I wait to hear back from ex's lawyer, and try to resist the temptation to phone every 30 minutes to see if there's been a response. I know I should leave it for at least a week before following up. Fingers crossed!