MB, I am not one of the Big Brains here with extensive expertise, so take everything I say with a ton of salt. Certainly you need to hear from folks who really know fisheries before making any changes!
That said, here's my two cents: When bass get big, they get harder to catch on artificial lures. This is especially true of Florida bass but it is generally true for all LMB types.
HSB may indeed compete for open water shad, but from what you say the Tigers already chow down on them.
Perhaps you could consider adding Northern strain LMB. They are more aggressive & will compete with the Tigers directly for food. I've heard that this forces Florida bass to be more aggressive, though I've never seen definitive research proving that.
They will crossbreed with your Tigers, of course, so you will go from F1 to Fx in your BOW. You will have to judge whether that is something you can live with, but in your shoes I'd sure consider the Northerns.
Otherwise, I suspect there is no alternative to live bait fishing. That can be fun, so I'm not knocking it, but it isn't everyone's cup of tea.
Please let us know how it goes. I'm in the process of getting my own pond built in east Texas and have considered Tigers myself, so am very interested in your results!