Go through insurance. Windshield comp losses in Florida should have no impact on rates. Had a similar issue with a rock chip last year and no change after filing a claim.
GA is different than FL. No 1st party diminished value (DV) in Florida. Your best bet is the appraisal route you are already on. What might help as well is stressing the relatively low number of these cars on the road and how one with $31k in damage is going to stick out come resale time.