I'll spread the net a little wider in area. With your dive count, I don't think the shark feeding dives out of Jupiter, FL, are a good idea yet (at least when tiger sharks are likely to appear).
You didn't mention whether a liveaboard would be an option for you. That might open up some things.
1.) Little Cayman (and I would think Cayman Brac) might have some reef sharks; some reef sharks diving the Caymans via liveaboard (ditto the outer atolls of Belize via liveaboard). Little Cayman also had Nassau grouper that were quite approachable. I wouldn't call it a big animal destination, but very nice for coral reef, and perhaps enough rays, reef and nurse sharks, big grouper and sea turtles to please you.
Cayman Aggressor IV May 2016 -
Trip Report - Cayman Aggressor IV Trip May 2016
Sun Dancer 2 (Belize) May 2015 -
http://www.scubaboard.com/forums/li...ving-belize-via-sun-dancer-2-may-2nd-9th.html
2.) Morehead City, North Carolina - seasonal but a good chance to get close to fairly big, scary looking sharks without baiting, that are highly unlikely to harm anyone (assuming you don't grab one or something similarly idiotic). You need AOW and nitrox, and dives are deep and short, it's wrecks not reefs, but scores on big animals.
Morehead City, NC August 2015 -
http://www.scubaboard.com/forums/no...us-dive-center-aug-9-13-2015-trip-report.html
3.) Jupiter, Florida - the goliath grouper aggregation in fall or lemon shark aggregation in winter. Not a place I'd go if coral reef was my end-all, be-all, but for really big grouper and/or some fairly big (but usually harmless) sharks, a good option.
Jupiter 2014 -
http://www.scubaboard.com/forums/florida-diving/491927-jupiter-trip-report-9-7-14-9-11-14-a.html
4.) Cozumel, Mexico - not a 'big animal' destination, but with nurse sharks, green morays, some sea turtles, eagle rays, occasionally big grouper, I'd say it's an excellent Caribbean destination with a decent array of 'medium' animals.
Tres Pelicanos & Casa Mexicana, Cozumel Sept. 2018 Report -
Tres Pelicanos/Casa Mexican Trip Report Sept. 2018
My Research Notes from Planning Cozumel Trip -
My Research Notes from Planning Cozumel Trip
But if your attitude is 'go big or go home,' and you can do without lush coral reef walls, Jupiter or North Carolina rock. Plus you may see some things a bit different than you're used to farther south.