Here is my suggestion, based on two weeks with 2 days in Orlando for theme parks.
First, see if you can fly into Miami and depart from Orlando. This sometimes is just as cheap or not much more expensive than going in and out of the same city and will be much better for the itinerary below. This is just a suggested itinerary, I am not recommending particular operators or guides. If you want suggestions for any of these, please say so or pm me. For the Keys, look to Netdoc, as that is his home.
This itinerary will echo some things you have already heard—mainly, best to concentrate your trip in South Florida. Ditch Naples altogether. Less time in the springs/Crystal River in favor of the reefs and wrecks in the Keys and Southeast coast.
Arrive in Miami and if possible get down to a hotel in Key Largo that same day.
Full days 1-2
Key Largo dives: various reefs, wrecks of the Spiegel Grove and Duane. The wrecks are deep (nitrox is essential) so do those in the morning and shallow reefs afternoon. Get in a night dive if you can on the reefs. These are fantastic shallow colorful reefs with lots of tropical reef fish, huge schools of fish, and a multitude of hard corals. Lots of animal life, but the “big animals” and macro stuff will be more in West Palm (below). The wrecks, though, are spectacular, far larger than any of the wrecks farther north.
Day 3: Morning, drive to Key West and get an afternoon trip to the Vandenberg. Alternative would be to drive to Key West after your afternoon dive in Key Largo, but it is a beautiful drive best done in the daylight. Overnight Key West.
Day 4: Get a morning dive to Looe Key on the way back from KW to Miami—probably the best shallow reef in the Keys and a great dive after the Vandenberg. Overnight in Miami, or, if you can do it, get up to West Palm Beach.
Day 5-7 (or 8)
Three days of diving in West Palm/Jupiter. THIS will be your “big animal” AND your “nudibranch” diving. Dive the wreck of the Castor, MG-111, Zion wreck trek, or other local wrecks for Goliath grouper where you can see dozens of 300-600 pound fish congregated on the wrecks in August. Again, these are deeper reefs and wrecks and Nitrox is essential. The reefs will have lots of turtles as well. Also pretty common to see some reef sharks. One essential dive is Blue Heron Bridge. This is a, seriously, world class macro dive where you might see things that people go to Indonesia to see. It is shallow (8 to 15 feet) and a steel 100, available at the local shops, can get you almost three hours of bottom time. This is an easy do it yourself beach dive, but I highly recommend you hire a local guide who dives there several times a week and knows where the best critters are at any given time—well worth the modest cost.
Day 8 Drive to Crystal River and use that as base for the springs/caverns. August is the absolute worst time to see manatees. Call Birds Underwater and they will be very honest as to whether a trip is worth it. If not, you can use High Springs or Gainesville as a base as they are closer to most of the springs. You could also stay in Orlando and do long day drives to the springs.
Day 9-10 Various springs/caverns. Blue Grotto, Ginnie, Devil’s Den. Alexander is also fun, as Netdoc suggested. Honestly, these springs and caverns are nice but two or three will be more than enough as they tend to be pretty similar. This is not the spectacular formations of the caves, mainly just caverns with unremarkable limestone rock walls, very little life, but super clear water. Might be fun snorkeling the Ginnie springs run. You could do a cavern course, if you don’t have that specialty already.
Day 11 Go to Orlando, only an hour and a half from Crystal River, two hours from Gainesville.
Day 12-13: Disney World (yuck)
Day 14: Drive to Miami for your flight. This is why it would be much better to leave from Orlando, you save 4-5 hours of driving to the Miami airport.
You can see that this takes up 14 of your 16 days, giving you some flexibility for more Theme Park/tourist time, more Keys time, or more West Palm time. Panhandle is not on here as it is too far away. There is an oddball dive in Venice, Florida for fossil shark teeth, but it is zero vis muck diving, not my cup of tea.
This is really the best of the best if you haven’t been to Florida before. The three wrecks in the Keys are spectacular. The Castor is great, as are some of the other West Palm wrecks, with the bonus of the multitude of big fish (which the Keys wrecks will not have).