It sounds to me like you are doing everything you can to find this payment. Your bank should (with a little encouragement in person) be able to find the archive of the check(s) that would enable you to show proof of payment. While doing this you could petition the court to forgive the fines. When you appear before the judge(s) you can begin to explain this process and all the things you've gone through to prove these fines were paid. I imagine after all this time the judge(s) would give you some relief.
At the same time, I imagine your best bet is your bank. Keep trying to get them to look in the archives for those cancelled checks. Also keep in touch with the clerk of the court(s) and politely ask them for guidance on how to straighten this identity issue out. His fines were probably entered under his name and birthday (since his license did get reinstated) but there must be multiple entries for him (which happens from time to time).
Feel free to reply as I'll be happy to help you brainstorm for more ideas!
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