His obligation is unchanged. If he doesn't do the job, or becomes inaccessible, call the Florida Bar and ask them for help. The DPR does not regulate lawyers and is the wrong place to turn--only the Florida Bar can discipline lawyers.
But the first thing to do is sit down with him and talk it out. If he has no time, ask for a refund of the fees.
If you know who the legal malpractice carrier is you may write them directly and put them on notice of a claim. I would consult a legal malpractice lawyer before doing so given your current representation.
The reality is that this is not going to be removed. Not to mention the state's practice of selling all of the court data to private companies which guarantee it will be in the public domain for life. It is a frustrating thing since many of these injunctions are filed just to gain an upper hand in a pending divorce.