This is coming from relapse lady (me) so I hope you know it contains no judgment whatsoever. Your desire to text him "one last time", and the way you are rationalizing the reasons for doing it, sound like your AV (Addict Voice) at work.
The AV keeps the alcoholic drinking. It's the little voice that says things to a sober alcoholic like "It's okay to have just one drink. It's your birthday for G-d's sake, treat yourself. It will be your last one."
Let's just be honest here, again with NO judgement. You were very clear in your text about him not contacting you unless he was in recovery. He has repeatedly disrespected your request and has tried all the typical A tricks to manipulate you into contact. He is dating online again, Sadie! Doesn't this in itself indicate that the relationship is over in his mind? Didn't this one fact alone absolve you of any responsibility to provide him with an official break up?
I just don't think your desire to formalize the break up, especially in light of his online dating activity, was coming from a genuine desire to do the right thing or have closure. I feel like it was your AV telling you "Maybe if you write him just one last time and tell him he has to recover, he will actually do it this time. He obviously misses you, he's texting everyday. And you miss him terribly. It's just one text."
My AV led me down the path to full blown addiction. I told my ex no contact unless he was in recovery. When he couldn't get me back any other way, he started to FAKE recovery. I bought into it because I didn't have SR and I wanted more than anything for it to be real. He went to AA meetings to shut me up, while continuing to drink the entire time. This went on for three years during which time I got SO addicted to his addiction that when he finally chose alcohol over me at the end, I was practically a broken woman.
I know how much pain you are in and I know how hard it is to accept losing someone you love THAT much. My heart truly goes out to you.