First I am not a lawyer nor do I have anything in Florida so I do not know Florida law. However there are some things that I did not see mentioned.
1: Have you been given anything that is signed by the tenant stating that they have turned their security deposit over to this LLC? Or is it just a letter from the attorney saying that they did? Your lease was with the tenant, not that LLC and anything that LLC sends you might not be valid.
2: Your lease was with the Tenant. It is a contract between you and her. She can not unilaterally change anything in that lease. Thus her "assigning" her deposit to the LLC might not even be something that she can legally bind you to. Just like when there are multiple tenants on a lease they can't just take someone off or add someone to the lease. I don't know that she can legally put the LLC in her place for the deposit.
3: Typically for lawsuit purposes sending someone a notice via regular mail will not count as service. If they didn't send it in some way that they have proof of service (Certified, Return Receipt, UPS, FedEx, etc) then it won't count as service. Anyone can stick a letter in an envelope and take a pic and say you mailed it but then never actually put it in the mail.
4: The little bit that I have had to deal with stuff like this in court I believe that anything that the opposing party files with the court, not only do they have to send to you as well, but the court upon accepting it then sends you a copy as well. If the court did not send to you a copy of what they filed on the 24th then the court may not even recognize it as valid.
Personally I would look more into #2. The LLC is not part of the lease and thus has no rights or claims to anything regarding the lease, unless you ever signed something agreeing to the LLC to become part of this transaction. Thus they would have no standings for a claim. Find out if they even have the right to assign their security deposit to someone else.
Spend the $200-$300 for a half hour consult with a RE attorney and get their opinion. If they tell you that you have nothing to worry about then you can rest easier than all of us non attorneys telling you stuff. It sucks paying the $300 but better than paying the deposit to that LLC.
I know you probably have a pit in your stomach over this and are losing sleep worrying about it and stressed out. Stupid stuff like this is one of the reason many get out of the Landlording gig. Everything you are feeling is normal. In my many years of this (property management company for over 20 years) I have dealt with similar stuff a handful of times and I still get the pit in my stomach and sweats while my stubborn side says do not cave in when we know we are right. Stay strong. It sounds like you did the right thing and you don't live in CA where even doing the right thing you can be screwed.