If the LLC has had no income for the last 2 years why would you care if the LLC has a judgment against it? The creditor would, absent fraud, self-dealing, etc., only be able to go after the assets of the LLC to satisfy the judgment.
You say you are one of many members so single member LLC liability issues would have no play. The only big issue is whether the LLC has any assets. If it has assets then that's really different and your approach would be too.
I would not file bankruptcy for the LLC if it has no assets and money. If the LLC did file bankruptcy for some reason you would not have personal exposure on the debts (absent many facts about its operation and whether you guaranteed any of its debts), and this would not be reported as a personal bankruptcy unless you signed a guaranty that you did not or would not want to honor.
Go speak to a corporate lawyer in FL regarding this.
Disclaimer: I am offering this information for educational purposes only. I am not your attorney. You should speak to a lawyer in your state.