Hi David -
Many alcoholics actually want to stop drinking, but they can't.
Even if your handyman isn't drinking or doesn't have alcohol on his breath, alcohol continues to affect his thinking, which makes him crafty: he will say what you want to hear. So, sure - he'll tell you he feels better when he doesn't drink, but he continues to drink. Drinking masks a pain he doesn't realize he has.
Hitting bottom seems to be a turning point, but no one knows what that bottom will be. In my dad's case, it was watching his alcoholic girlfriend neglect her son. He had done the same to his children, even worse. After more than 35 years of drinking, decades of attending AA meetings, going on and off the wagon, he had lost his family, his job and his self respect. By all accounts, he had reached bottom many times. But the simple act of his girlfriend asking him to take responsibility for her son made him realize what he had done to us. And so, he stopped. Just like that. It wasn't easy, but he stuck with it.
Alcohol is a terrible mistress, and my father didn't even like the taste of booze. Having expectations of someone who is in its grip is like asking an amputee to grow another arm or leg. An alcoholic may function normally for the most part, but until he's ready to begin real treatment, he can't be helped.
I wouldn't stop trying to get him to a dentist. You can continue to try to get him into treatment, but know that you may be beating your head against a wall. No matter how big your heart is, just know that it's *his* problem, not yours, and your first responsibility is to yourself.
Good luck.
Marlene