TALLAHASSEE — Florida regulators Thursday dug into a proposal that would lead to double-digit rate increases for customers of Citizens Property Insurance Corp., as the state insurer of last resort continues trying to push policies into the private market. The Florida Office of Insurance Regulation, which would have to sign off on increases, held a three-hour hearing on the proposal, which in part would lead to an average 13.5% rate increase for the most-common type of Citizens policy, known as homeowners’ multi-peril coverage. That would translate to the average price of homeowners multi-peril policies going from $3,560 to $4,041, said Brian Donovan, chief actuary for Citizens. Other types of policies would see varying increases, but all averages would be in double digits.