Just IMO, one of the best things you could do would be to let go of the idea that you're "codependent." That's not a real thing. You're not unwell for caring about someone who is unwell.
If that seems like a big leap, consider -- the whole deal began when the wives of alcoholics were labeled "co-alcoholics" to convince them that they, too, needed to turn their wills and lives over to God. That morphed into "co-addicts" for addicts of other drugs and then into "co-dependents" for one and all. The original term is now so distant that we can see it for the silliness it is. Surely you don't believe that you and your boyfriend are co-alcoholic together.
The loved one of an alcohol addict is no more a codependent than the loved one of a cancer patient is co-cancerous.
I'm sure you know that you can't
make him do anything. It's good of you to care about him, and kind of you to support his efforts to break the addiction. You've given him the book -- I might have suggested something shorter and sweeter, but he has the book now. The information is there.
If his army of sponsors and counselors allow him any contact with you, your primary goal should be to reassure him that you love him. It sounds like you've got that part down pretty well.

If you mention extinguishing the addiction, they'll only go back to forbidding contact with you because you're encouraging him to drink.
You mentioned that you think you'll have to break up with him if he doesn't recover. That is fair enough, and of course you have to take care of yourself first, but could I encourage you to hang in just a bit longer? When he falls off the Step wagon again, you can be there to suggest that he might want to try something else since the Step approach isn't working.
It's tough, I know. My husband is my hero.