Seeing as there is no gun registration in Florida I don't see how any could be registered to you. The only record of any purchases would be on the 4473's and the bound book with the FFL where you bought them. Make model and serial number are not reported during the background check.
If the FFL is now out of business the records would have been tansfered to the BATFE. Who knows what the BATFE does with them but by law they are supposedly prohibited from creating a defacto registration.