I recall that the one time I saw a situation like this first-hand was when I was assisting in interviewing several years ago for some open positions at the child mental health facility where I was the CS. One nurse came in for her interview with a whole stack of papers which she spread out on the table we were sitting around for the interview (she, the program manager and I).
She told us right up front that she had become addicted to drugs (and, in her case, she had gone on to dealing them, had lost her license, and actually was convicted and did prison time for the dealing! So it sounds like her situation was much worse than yours ...) She then walked us through all the paperwork -- which was documentation of her successful completion of a drug treatment program, results of the monitoring by the BON in the state where all this had occurred, results of the ongoing monitoring in our state, references from clinicians in her drug treatment program and her sponsors in her on-going relapse prevention program, references from past employers, documentation from the BON about the reinstatement of and restrictions on her license and how long that was expected to continue, etc., etc., etc. -- anything she could think of to document that her ongoing recovery was successful.
She was not defensive or evasive about her situation at all, but was v. open about the mistakes that she had made, AND all the work she had done to overcome them. We were v. impressed with her honesty and initiative, and we did hire her.
I know this is a v. difficult situation to be in. In addition to talking to potential employers about your history and current status, it may be helpful to assemble (as she did) as much documentation as you can of what you've accomplished in getting back on track and are continuing to do (if you haven't already done that, I mean ...) Best wishes --