I think you're making the right moves. You STBX is obviously nowhere near recovery and seeing as it's a progressive disease, you can expect it to get worse.
Can I ask if there's a specific reason that you're no longer comfortable with the supervised visits? Is he violent or abusive? Is he unstable? Has he ever been? If there were events leading up to your decision, it might be wise to document them clearly and succinctly in order to support your move for sole custody. The fact that you have only allowed supervised visitation up to this point is excellent.
I had pages and pages of journal entries documenting every single visit and contact I had with XH. It clearly indicated his instability and lack of interest in truly parenting DD, not to mention his alcoholism.
In my custody ruling, it is expressely indicated that I have discretion over visitation, meaning that if I find the situation unsafe for my DD, I can refuse visitation altogether. Would it be possible for you to include such a provision in your project of judgment, and hope that the court approves it?
In addition, when I testified before the judge I made certain to mention that I WANTED DD to see her father, but that he was an unreliable and unstable parent, so I needed to have some control over visitation. I also indicated that I had done everything I could to foster a relationship between DD and her father, even going so far as supervising the visits myself, despite how awkward it was. I believe the judge really looked favourably on my case because I didn't say I wanted to deny him all access.
I never got supervised visitation, but then my XH hid his alcoholism very well. He had no DUIs, no arrests, no stints in rehab and no job layoffs; he was very functional. However, given that I was granted discretion over visitation and that XH did not want to "bend to my requirements", he stopped seeing DD altogether, which is fine and dandy with me.
I also wanted to mention that because I was dealing with an ex-partner's *alcohol* abuse--and alcohol isn't illegal, it was up to me to play "booze police". Had XH been a cocaine or a heroin addict, it would have been a whole other ballgame. I think the breathalizer is a great tool; perhaps you can specify that the person supervising the visitation will be administering it, so that your STBX cannot claim that you tampered with the device.