UF: you must wait 12 months to reclassify as a FL resident. I need documents such as a FL Driver's License, Voter ID, Motor Vehicle Registration, etc. all dated 12 months prior to the first day of classes of your second year (e.g. if the first day of class for your 2nd year is August 1, 2020, all your documents should be dated before August 1, 2019).
As for Stony Brook, I'm not sure since I was a NY resident, but I turned them down because of the lifestyle of the area. I was constantly bored on weeknights/weekends/days off in undergrad, it was impossible to get anywhere without a car (not that you'd have many places to go besides the grocery store), the weather is bad half the year, etc. Fine for academics (medical school curriculum), but not for me. Please reach out if you would like to discuss.
You can get FL resident status, but it will be next to impossible to get UF Resident For In-State Tuition Purposes. Not sure about Stony. I have heard people get it after a year?