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I dont think you do eviction at all since they moved and turned in the keys.
In additiona to carpet and cleaning fees, go after them for future rent ....
I would go after them for rent until the end of lease or until you rerent just like any tenant, since they did not give move papers. If you rerent prior to the end of their lease, charge them for the rerent fee(agent, advertisement, etc)
since you are in FL, make sure you send proper notice of intent to withhold security deposit. Must do this in writing within 30 days else you forfeit right to keep sec deposit monies.
Also give them notice of rents owed until end of lease or until new tenent found. sue them as needed. It will go on public record and another landlord will at least be forewarned.