Charged ~$1,000+ In "late Notice" Fees After Leasing Office's Own Employee Accepted Our Move-out Paperwork With A Missing Signature And Never Told Us For 6 Weeks

Location: Florida

TL;DR: We signed a lease close-out/move-out agreement with a leasing office employee well before the deadline. Turns out the employee forgot to have my mother co-sign it, but nobody told us for ~6 weeks — we only found out when my father happened to be back in the office for an unrelated reason, by which point the "deadline" had already passed. We were verbally told there'd be no fees and the paperwork would reflect the original date. We're now being threatened $1,000+ for "missing the notice deadline." The property manager is blaming my father for not knowing who needed to sign, and has now cut off communication after a tense conversation. Looking for advice on next steps.

Timeline:

(6/09): My father receives our lease renewal letter from the property manager.

A few days later (~2 months before the notice deadline in our lease): My father goes to the leasing office to start the close-out paperwork for not renewing. A staff member (not the manager) fills out and signs a close-out agreement with him. She does not fill in a date, but does print him a copy for his records. (Document 1 — signed, undated.)

Staff told my father this completed the process.

(7/28): My father goes back to the office about a possible unit transfer, decides against it. During this visit, he's told for the first time that the earlier paperwork was incomplete — it also needed my mother's signature. This is roughly 4–5 weeks after the notice deadline had already passed.

Since my parents' restaurant is under a mile from the office, my mother comes in within minutes and signs. Staff verbally reassures my father there will be no fees and that the paperwork will reflect the original signing date. (Document 2 — same agreement, now dated and with the second signature.)

The only two emails we received in the prior 6 months were (1) the original lease renewal notice, and

(2) move-out instructions, which were sent the evening of our actual move-out date — too late to schedule the required walk-through. (Documents 3 & 4.)

Shortly after move-out: We're charged $1,000+ in fees for "failing to notify by the deadline."

Yesterday: My father and I met with the property manager to dispute this. She said tenants are responsible for knowing who needs to sign lease documents, and claimed staff did tell my father about the missing signature at the first meeting — which doesn't line up with the facts (my mother works five minutes away and would have come in immediately, as she did the second time; the staff member also signed and printed a copy of a document she believed was complete). When I pushed back on this, the manager became short with us, said she could no longer help "due to disrespect to her and her staff," and ended the conversation. She mentioned she'd email her boss, but as of now we've heard nothing further.

Documents we have: the original signed-but-undated close-out agreement, the later signed-and-dated version, the lease renewal email, and the move-out instructions email (with timestamps).

My questions:

Given that a staff member accepted and signed off on the paperwork before the deadline (even though it needed a second signature we weren't told about), do we have a real argument that timely notice was actually given?

Does it matter that we were verbally told there'd be no fees and the date would reflect the original signing?

What's the right next step — demand letter, corporate escalation, small claims, something else?

Happy to answer questions or provide more detail.