Ruby notes - "You can ask him to move out and still support his efforts."
I think you are wise to stop the wedding. Entangling yourself legally while you're both still catching your breath from a major relapse would not be a good choice.
However (and this is my little spark of optimism speaking here), it is not as though your boyfriend had spent these last 3.5 years in and out of recovery. The way I read your story, he was doing his "own version" of moderating for most of that time, until he finally went through in-patient and out-patient treatment. That makes this his first official relapse.
Everyone's recovery looks very different, but there are plenty of people with years or decades of sobriety who did relapse at some point in the process. He is not a hopeless case. His intent and follow through in completing that amount of concrete treatment is laudable; he is definitely making an effort, although not entirely "successful."
If there are aspects of this relationship which are important to you, and if you are not yet ready to be "done," then I think you need to be self-protective and intentional with how you sculpt its form. For me, that would mean strict separation of finances (and probably living space). I wouldn't marry someone (or share a financial or legal future - ie. having children, buying a house, etc.) until they had considerable continuous full sobriety under their belt. As you know, even considerable sobriety is no guarantee, so any major decisions will have to be put through the "do I want this for myself and can I handle it entirely alone if that's how it turns out?" evaluation.
You can ask him to move out and still support his efforts. You can ask him to move out and still enjoy his company. You can ask him to move out and simply see what happens next - for you and for him.
If you want a marriage or partnership which does not have these constraints and limitations, he is probably not the best candidate, and you might have to let him go with love and best wishes.
You get to pick what you are looking for in a partner. For lots of people, marriage or children are not something they want or care about. If that is the case, there is a little more flexibility in what the relationship looks like.
It has been very useful to me to really spend some time thinking, journalling, and talking about what I'm actually looking for. A year ago I would have said that I wanted to get married. After a fair amount of thought, I realize that I'm open to a relationship that doesn't culminate in marriage. For me, marriage represents financial safety, which was a goal long ago. I'm secure financially through my own efforts at this point in my life. As we change, the things we want and need from the world change also. Make sure you're not fighting for a model that isn't actually that important to you. And if you discover that this is important to you, then you can filter your decisions about who to be in relationship with through that deep and conscious necessity.