So far, the DCA hasn't said whether Crump will be allowed to respond. Backwell cites
Towers v. City of Longwood, 960 So. 2d 845 (Fla. 5th DCA 2007), where a third-party was allowed to respond in similar circumstances. But that was a civil case, where parties are allowed to intervene for limited purposes to protect their interests. I've tried (within my limited abilities) to find a similar example in a Florida criminal case, but couldn't. I also suspect that it hasn't happened too often in civil cases, or Blackwell would have chosen a different case to cite.
Towers seems to me to be very favorable to the defense's position on granting certiorari when a deposition isn't allowed.
Crump's motion to respond was unopposed, and there's certainly an argument that the party who's most affected should have a say. On the other hand, it doesn't seem to be specifically allowed by the appellate rules, and Crump's work-product arguments are already part of the trial court record, and were include in the defense's appendix. Even if Crump is allowed to respond to the work-product argument, I don't think he should be permitted to argue on whether the petition should be dismissed because of the availability of post-judgement appeal.
I think that Crump's continued interference with discovery in the criminal case, by pretending that the law applicable to civil cases applies, and by moving to intervene in the appeal, actually helps the defense. The time is now ripe for the defense to reply along the lines of your prior observation as to the different sources (criminal vs civil rules - absence of common law privilege in Florida) of attorney work product protection in civil and criminal cases and the fundamental constitutional rights of a criminal defendant trumping Crump's purported privilege.