How can I preserve 2" x 9" wood slabs in the Florida climate?
Paraffin is a low temperature wax (around 100 F) that is inexpensive and can be melted in a pot (or disposable aluminum baking pan) to allow dipping.  Its brittle at room temperature, so your slabs must be handled gently after dipping.

It is best to dip just the end grain ends of the piece and leave the other 4 sides alone.  Keep them out of the heat and sun, a root cellar would be perfect.  (probably not an option in FLA).  Perhaps a cooler, this will let them dry very slowly, a key to minimizing splitting. 

Addendum:

It is usual to make the original piece a bit oversize and then mill it to the final size after it is dry.  This is why a 2 x 4 is 1.5 x 3.5, a combination of shrinkage and final sizing.  

This will allow you to trim the top and bottom so that they are parallel and will hold the vase steadily.  A block plane or sander can make one side flat and a thickness planer will make the other side parallel to it.