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You would want a civil litigator (trial lawyer) with experience in suing government agencies. Most civil lawyers in general practice have had experience in this area. If you don't know where to find such a lawyer, contact the Florida State Bar Association's lawyer referral service. They charge a fee of around $50 which includes a half hour free consultation with the lawyer. You can also try a private referral service such as Martindale.com. Many of Martindale's lawyers are peer and client rated to help you narrow down your options.
The American Civil Liberties Union would also know lawyers who routinely sue the state/county/agencies as many of these cases are civil rights cases. The ACLU has branches throughout the state and may offer you some direction if you have difficulty finding someone local who wants to go head to head against the authorities.