sandbar shark.

I'm convinced that this is the shark we saw:

Sandbar shark (Carcharhinus plumbeus), also called the brown shark, is found nearshore typically at depths ranging from 60 to 200 feet. It is both a predator and scavenger, feeding chiefly near the bottom on fish and shellfish. It migrates long distances and matures at about 6 feet in length but can reach a maximum length of nearly 8 feet. It is brown or gray in color with a white underside. It migrates south in schools to Florida waters during the winter. Some remain throughout the year. This shark accounts for about 60 percent of the state's commercial landings. -- University of Florida, IFAS

I know that we will never know for sure, but I have been researching sharks commonly found in Florida waters. The Sandbar shark accounts for 60% of them, looks most like the dorsal fin that we saw, is dark in color which is accurate to what we saw, and is found nearshore. I'm pretty convinced.