I don't know how it is in Big Cypress, but on the Wilderness Waterway that N2S referred to, camping is only allowed at designated sites that must be reserved when your permit is issued. You may just have to settle for what is available. Also, I know pedestrian traffic is forbidden in most areas, particularly the hammocks (that's hammocks as in small islands of non-mangrove trees, not as in sleeping nets).
I, too would discourage you from trying to use a filter for water. The water is going to be brackish (part salty) nearly everywhere you go, and if you do find fresh, it will be absolutely thick with silica and tannins. Even tabs aren't going to help you in the 'glades. You will need to pack in your water, I'm afraid. One to two gallons per person per day.
Also, a close second to the mosquito menace will be the RACCOONS! They are fearless, numerous and they want your stuff! Take a slingshot or a tazer. No kidding.
Enjoy your trip, and take some pictures!