The company can't force you to settle out of court. But if it pays you what it says you owe it in an unconditional payment, it can cause your claim to fail on the merits at trial for a lack of damages.
A company might want to do this to avoid the collateral estoppel consequences of a judicial determination of your liability. The doctrine of collateral estoppel would make judicial determinations on the merits on particular issues resolved in the case against it binding on the company in future lawsuits against other plaintiffs.
A company cannot simply pay to defeat a claim on the merits, however, in a class action suit, without paying all of the amounts owed to all members of the proposed class.
Some states also have procedural penalties such as costs or attorney fee shifting when a settlement offer is refused and the outcome at trial is not significantly better than the settlement offer, but I don't know if Florida has such a provision. If it did, your net win could easily be converted to a net loss.