OK, I may catch some flack for saying this, but I think you're screwed, unless your building inspectors and code enforcement is much,
much more-lenient than they are here.
I am also in Florida, in a metropolitan area, and I assume you are too. Bottom line, I doubt you will be able to get approval for something installed without current code compliance to the Florida Building Code. You need to have a talk with the AHJ and ask them, "what's required?" I see you did mention some aspects of the issue. Did your local authority having jurisdiction give you a zoning notice of violation or was it a building inspector? The first thing I would do is to request an official copy of the history of permits let for your house since its construction. You can probably go-back a few years, to the point where they began putting records on the web, but data before that may need to come from a hand-search of documents, and the jurisdiction is allowed to charge you for the staff time.
Here is the problem: your original installation was probably done without the full permitting, inspection, and final approval being done,
back-then. Getting something that-old permitted after the fact is not likely going to happen. Stay in non-compliance, and they can lien your property, and in short-order, you may find yourself facing a bill of many thousands of dollars. Failure to comply at a rate of fining you $100/day, it would become a fine of $6,100 by June first, if the fine imposition was to begin April 1, and that's no-joke! Don't come-into compliance, which is the only way once the fine starts, to stop-it, and they will file a lien with the county clerk of the courts, and update it periodically. If your property is homesteaded, they cannot force you to sell to satisfy the lien, but if it isn't, well, you better get an attorney.
I suggest you buy a premanufactured shed sized to fit your permitted space. It's not-uncommon for a municipality to prevent anything over 200-250 square feet for a stand-alone shed. Your 'add-on' was probably enough to meet your zoning code allowed maximum square footage, combined with your original shed (120 + 80=200 sq. ft.).
You may live in a HVHZ (high-velocity hurricane zone) area, and the Florida Building Code has very specific requirements for withstanding wind load, uplift, and overall building requirements. Your fourteen year-old shed didn't meet the requirements then (not permitted/approved), and it certainly doesn't meet them now. The FBC has undergone numerous changes since then, and you have to comply with the version of the code adopted by your local governing body, the building dept. That is a specific year of the Florida Building Code, as adopted by your local government (village or city, or county, for example if you live in an unincorporated area) in their ordinances, codes, and standards. Your old building would need to comply with current code, not the FBC of when it was first installed, since it wasn't properly-permitted back-then.
I'll suggest you look at the products made by Lark Sheds, they are built in GA, and they have Florida Product Approval, which is what you want and need. I got one from them recently, a 10' X 20' shed, 18 ga. steel frame, sheathed w/PT plywood and Hardi-Board, and a steel roof, designed to meet wind loads of up-to 175 mph.
http://www.larkbuilders.com/ Find a local dealer, and see their products. They aren't cheap, but if you compare them to your options, they will stand on their own merits.
I am a plans examiner, a Life Safety Code Inspector, have worked as a planner, and have done many permits and inspections for this type of situation. You are going to find it's probably expensive and frustrating to try to permit what you already have. A Professional Engineer (P.E.) won't 'ink their stamp' for less-than $500, and they would have to do a forensic exam of your 'as-built' which will cost time, and do the calcs, to be able to say that your installation meets the current code. My friend who is a P.E. charges $100/hour, travel time not-included.
Either demo it, or sell it 'as-is, where-is' and be sure your homeowner's insurance will cover someone trying to dismantle your old shed should you sell it; or save yourself the liability and demo it. Then get an approved premanufactured product installed, and go-forward without having undergone a lot of frustration , effort, and expense.
Also, if you live in a designated historical district, your options are going to be limited by the ordinances protecting the district. Contact the zoning dept. for more information. The same goes if you abut wetlands, there are requirements which limit your developable area. Again, contact the zoning dept.
http://www.cityoforlando.net/code-enforcement/
https://library.municode.com/fl/orlando/codes/code_of_ordinances
https://library.municode.com/fl/orl...PRARDE_PT6TRDEST_APREREOFUSREOFDI_S62.605SPST
https://library.municode.com/fl/orl..._PT5ACUSST_5BSPACUSST_5B_6_GAYASA_S58.934GERE
PART 5. - ACCESSORY USES AND STRUCTURES
5A. - GENERAL REQUIREMENTS
Sec. 58.901. - Accessory Structure Location and Zoning Standards.
Note: It looks like Sec. 58.901(h) addresses square footage. You will need a sealed survey, probably, to permit whatever you choose to do. At the least, that can be used to tell you what size you can have for your accessory use outbuilding. You include a sealed copy of your survey, and make a to-scale copy and draw on the copy for your site plan of the accessory building's location, to-scale. You probably have to submit two-copies of all your docs, one stays with the city and will probably end-up digitized, if they don't require submittal of plans in that format to-begin. The other will be yours, the homeowner's copy and needs to stay on the job, for retrieval by the inspectors for their scheduled inspections.