While yes, it all seems very disingenuous because you've heard it a thousand times (as many here have), it doesn't hurt anything at this point really, since you aren't holding out great hope.
He basically has 1 month to show you whether or not he means this. Now that doesn't mean that you actually have to do anything other than what you have planned, which is to move out or have him move out.
Hopefully, even if he isn't successful it won't turn in to a great pity party or have him venting his frustration outward at you. This can turn on you, the blame for "forcing" (even though you re not) him to do what he may not actually want to or can't do.
I'm posting a portion of an article I post to a lot. Not because it is the bible of addiction just that these behaviours of the addict are well worn, predictable in many cases. So it gives you some idea of what might be in store because isn't everyone tired of being blind-sided.
"One of the most damaging interpersonal scenarios occurs when the addict, usually as the consequence of some unforeseen crisis directly stemming from his addiction, promises with all of the sincerity at his command to stop his addictive behavior and never under any circumstances to resume it again.
"I promise," the addict pleads, sometimes with tears in his eyes. "I know I have been wrong, and this time I have learned my lesson. You'll never have to worry about me again. It will never happen again!"
But it does happen again and again, and again, and again. Each time the promises, each time their breaking. Those who first responded to his sincere sounding promises of reform with relief, hope and at times even joy soon become disillusioned and bitter.
Spouses and other family members begin to ask a perfectly logical question: "If you really love and care about me, why do you keep doing what you know hurts me so badly?" To this the addict has no answer except to promise once again to do better, "this time for real, you'll see!" or to respond with grievances and complaints of his own. The question of fairness arises as the addict attempts to extenuate his own admitted transgressions by repeated references to what he considers the equal or greater faults of those who complain of his addictive behavior. This natural defensive maneuver of "the best defense is a good offense" variety can be the first step on a slippery slope that leads to the paranoid demonization of the very people the addict cares about the most".
Addiction, Lies and Relationships