I would suggest contacting law enforcement to let them know that the at-fault drunk driver supplied you and the officer with false insurance information. Next you can contact the Florida Bureau of Financial Responsibility.
The sole purpose of the Bureau of Financial Responsibility is to ensure that people are responsible for their actions involving motor vehicles. This agency does so by making sure everyone has insurance to pay for the damages they cause, or they may cause, when they own a motor vehicle or register a motor vehicle.
This FL state agency will help you recover your damages and be compensated for your injuries if you have any. Their help page notes that if you are unable to contact your insurance agent to represent you and determine if the at-fault party is insured or uninsured you should obtain a copy of the final crash report and forward it to: Bureau of Financial Responsibility, Neil Kirkman Building, Room A212, MS-98, Tallahassee, Florida 32399-0585.
Request that the bureau process the crash. If the insurance company listed on the crash report has denied coverage, obtain a written letter of denial and attach to the report when mailing to the Bureau of Financial Responsibility.
If you have been involved in a crash and desire the insurance coverage for the other party, you may obtain the information by mailing your request to: Bureau of Financial Responsibility, 2900 Apalachee Parkway, Room A212, MS-98, Tallahassee, Florida 32399-0585.
You must include a copy of the complete crash report, front and back, or the driver exchange form. These forms will provide the department with the necessary information needed to expedite your request. You may fax the crash report to the bureau at 850-488-7444. They say to allow 10 working days for research and reply.
If you need more help with this process call the Department of Highway Safety and Motor Vehicles, Customer Service Center, at 850/922-9000.