It does not appear that Georgia has a "borrowing statute" that would require the court to apply the Florida limitations period - you should confirm that with a local lawyer, as I may have missed something. It does, however, potentially allow you to raise the defense of laches (undue delay); however I suspect that provision applies only to claims brought in equity as opposed to claims under law, and breach of contract is a legal claim.
Quoting Georgia Code § 9-3-3. Applicability of limitation statutes; equitable bar
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Unless otherwise provided by law, limitation statutes shall apply equally to all courts. In addition, courts of equity may interpose an equitable bar whenever, from the lapse of time and laches of the complainant, it would be inequitable to allow a party to enforce his legal rights.
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