I have a couple of pages on my website on how to calculate flotation. The pages apply to power boats but the principle is the same, and you most likely don't have a large chunk of metal (the engine) to worry about. http://newboatbuilders.com/pages/flot3.html
There are also pages on level flotation, but I think with a heavy keel you needn't be too concerned about that, the keel will pretty much keep it keel down as long as you lower the sails.
You have left out some factors in your calculations.
There are things you need flotation for:
The hull, (includes fiberglass, wood, metal such as mast, fittings etc. Wood is flotation, and so is other stuff like a hollow but sealed mast, empty tanks. )
People (each person will require some flotation especially if they are high enough to be out of the water - sitting on the cabin top?)
Machinery: I don't imagine you have an inboard engine, but you may have an outboard. You need enough flotation to float the engine.
Gear: All the crap you carry around in your boat such as food, water, fuel, batteries, stores, porta potty, etc. All that stuff can add weight or even be considered flotation. Coolers are great flotation, so are seat cushions, and foam mattresses.
It can be done. It is routinely done in France where all boats under a certain size must have flotation. The ETAP is a good example.
But I think it will take a lot of space, add significant weight to your boat (flotation foam weighs 2 lbs per cubic foot) and there are other ways to keep the water out starting with a good bilge pump, watertight hatches and companion way doors, big cockpit drains, good scuppers to drain water on deck, and last but not least a big bucket.
There is an old saying. The best bilge pump is scared man with a bucket.
Also getting to know your boat, how it sails, when to reef, how much it can heel before water comes on deck, and how wet or dry it is. The last is important because if a boat is wet (takes a lot of spray and water on deck) then the sailor is wet and miserable. A dry boat means a dry and comfortable sailor, and a nice sail.
But most important is the sailor, the person sailing the boat, and knowing their own limitations. There are hundreds of cases where the USCG rescued people who thought their boat was done for and they just couldn't take anymore. Then later their boat is found sailing all by itself and is just fine. It's not the boat that can't take it. It's the people. Know your boat's limits but more so know your own limits.