If you want to see tigers out of Florida, I think you're going to either accept baited/feeding dives (e.g.: Emerald Charters (
I dove with them, - trip report)), get
very lucky, or let it go. On the Emerald trip we saw plenty of bulls, but not really large ones up close. A few years back I was talking with a Captain on a dive boat elsewhere who'd done the
Bahamas Aggressor's Tiger Beach itinerary and I think he told me they used baiting (a triangle?) but not feeding. If that's of interest check and get current into.
I dove out of Morehead City, NC, to work my way up aiming for the tiger shark diving. Be aware not all tiger sharks are created equal; from researching for my trip, it was my understanding those seen out of Jupiter don't tend to be as large as some seen in the Bahamas (but the 2 near-10 foot females and slightly smaller male I dove with were big enough to kill ya, just say'in...).
There's another option for non-baited big shark diving that just sailed right over my mind for whatever reason, but may interest people who run across this thread. These are not cheap trips, but if you're willing to pony up for a bucket list trip, you could try:
1.) Socorros live-aboard - several to choose from, probably the cheapest option of these 4.
2.) Cocos Island live-aboard - you may see tiger sharks. 2017 And 2018 saw ‘issues’ with tiger sharks – one killed a woman and injured a guide Nov. 30, 2017 –
Death in Cocos from shark attack – and on April 28, 2018 one possibly ‘test bit’ the BCD of a diver at the surface –
German diver attacked by shark – Isla del Coco, Costa Rica – and Undersea Hunter live-aboard noted procedural changes due to risk concerns. Tiger sharks are a ‘feature’ of Cocos diving, but be aware.
3.) Malpelo - there is one active live-aboard boat, the
Ferox.
4.) The Galapagos Islands out of Ecuador, South American. Multiple live-aboard options.
So if you want cageless big shark diving, you've got a range of options (and part of the year Emerald Charters and some other local providers could scratch your hammerhead itch, albeit baited), even if you want unbaited natural encounters.