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Call the Department of Justice's Motor Vehicles division and ask if they'll suspend his driver's license with an Order of Contempt from the judge (ordering license suspension) or if you have to go through CESD. Their phone and fax numbers on listed here:
You may be able to file a Motion for Contempt, noting how little he has paid and how much he owes, and asking the judge to order that these licenses be suspended. But you want to make sure that the Department of Justice will enforce that before you spend the time and money to get the order. They may tell you that you have to go through CESD, in which case you'd want to talk to someone there.
Yes, if you can get Montana to take over the payments, then Montana can suspend his license. But unfortunately, it sounds like you don't have any way of doing that until after the trial. It's true that Florida can't suspend a Montana driver's license. They could suspend his ability to drive IN Florida, but that's not going to hurt him much.