Ok, brief chemistry overview. CaO, calcium oxide, "lime", is extremely alkaline. If you add one molecule of water (H2O) to calcium oxide, you get "slaked lime", aka calcium hydroxide, Ca(OH)2. Most people use slacked lime because it is less corrosive and somewhat easier (safer) to handle. If you run the water plant over at, say Ocala, you would probably add CaO to hard water (that contains calcium and carbonate) that makes the water alkaline, and the solubility of the calcium carbonate goes to almost zero, and it falls out of solution as a powder or sludge that is almost pure calcium carbonate, CaCO3. Calcium carbonate is a source of calcium for fields, but it is not very alkaline.
That is actually the trouble with calcium salts. They are generally very insoluble at neutral to basic pH. So, they don't go very far in soils. So while applying pelletized "lime" is easy, the alkalinity effects do not migrate very far from the pellet, especially if the "lime" pellet is calcium carbonate, rather than slaked lime or lime.
In an ideal world, you probably want to apply lime/slacked lime powder to your field, then disk it in to disperse it, and repeat until you get the soil chemistry to where you want it to be. The details of whether you will hit enough calcium or the correct pH first will depend on the details of your soil chemistry and which of the calcium products that you apply. Your county agent probably can advise you on the desired ratios of lime/slaked lime/calcium carbonate for your fields. It may be a bit iterative, depending on your soil chemistry, so I would be prepared for a few cycles. You are doing it at the best time because you can work the calcium deep into the soil, and neutralize a larger volume of your soil for a more lasting effect.
My fertilizer spreader came with a "anti-caking" rod that extends up into the hopper specifically to breakup clumps of lime/slaked lime powder. Not all spreaders have them, but my guess is that in Florida, it is a necessity.
Does that help?
All the best,
Peter