Don’t confuse EFC - expected family contribution - with COA - cost of attendance. Your EFC is what the financial aid formula says your family would be responsible for. Your COA is what you’d actually end up paying.
In your situation, you are looking for schools where your COA would be in the 10-20K range even though you have a 40K EFC. You’re going to have to apply to schools where you are quite overqualified, in order to get merit that generous.
Truman State in Missouri could be worth a look. It is the Missouri equivalent of NCF - the public honors LAC. It’s very affordable to begin with (about 25K/year “sticker price” for OOS), and you’d qualify for the max 8K/year merit, so it would be in range. It’s much smaller than the big FL publics (5K undergrads) but big enough to have a good variety of majors to explore.
At any school with a more typical “sticker price,” you’re going to need a full-tuition scholarship to get to your price point, since your budget will only cover room/board/transportation/expenses. Don’t bother considering schools where full tuition merit isn’t possible, or where your stats aren’t far enough above median to make you a viable candidate for one of those big awards.
Miami of Ohio would be a possibility - full-pay OOS COA is over 50K, but your stats put you in the auto-merit category to get at least 21K (which wouldn’t be enough) and up to full tuition (which would be enough).
When push comes to shove, bright Futures is hard to beat. You can always study abroad for a semester or a full year, and/or use the money you save to spend summers somewhere else. (Or a few of the FL publics participate in the National Student Exchange that places students on campuses in other parts of the US.)