Wow, deja vu for me reading this:
1. "The DUI doesn't count": my ex tried this one with a DUI that turned into a stayed charge (because of an ongoing and unrelated court challenge to the legality of roadside license suspension). He seemed to believe that the fact that he drove his car straight into a concrete median and was indisputably over the limit when the police got there and breathalyzed him didn't count - the only thing that "counted" was that this one incident did not result in a conviction on his record. (Fortunately, our court order contained the phrase "alcohol-related incident", which this clearly was, in addition to all the other police-involved alcohol-related incidents he racked up).
2. I too found out about this particular incident from a public source - it wasn't literally in the paper, but if you go to the courthouse with a name and a birthdate because you have a persistent feeling that something is off, criminal charges are a matter of public record. He was indignant that I was "invading his privacy". My view was that if something is public, it isn't private. And he was more than welcome to do the same thing, run my name and birthdate at the courthouse and see what came up.
3. "And I just have to hope he runs his own clock out before he can manage to get our kid in danger". That is exactly what happened - he ran out his clock, very much as your ex is doing now.