In Peninsular Properties v. City of Bradenton, the 2d DCA reversed the circuit court and held that a request for mediation under s. 70.51 (Bert Harris, part II) stays the 30 day window for filing for cert review. The circuit court had dismissed Peninsular's petition, holding that the statutory tolling provision was an unconstitutional invasion of the Florida Supreme Court's jurisdiction over procedural matters. The District Court reversed, holding (sensibly) that the statute provided a "mixed" substantive and procedural remedy, and that the purpose of the statute required that the time to file be tolled.
Right outcome, probably to the chagrin of the many, many local government attorneys who dislike (and try to undermine) the mediation provisions of the statute. I have been in the position of filing a 70.51 early, then filing a cert petition (or 163.3215), and then requesting that the cert review be tolled. I've had that request denied, which now would probably constitute an abuse of discretion.
The argument here focused on the procedural/substantive debate in treating the statute as "tolling" the time to file; Peninsular apparently did not argue the potentially easier argument: that the statute effectively tolls the rendition of the quasi-judicial order of the local government during the pendency of the meditation. Understood that way, the statute effects the actions of a state or local government agency or board and therefore doesn't even implicate the constitutional issues. Several decisions (not on this statute) interpret tolling provisions that way. This would have another salutary effect that is completely consistent with the intent of the statue: because the decision would be non-final, the local government would be in the position of "reconsidering" it in light of the special magistrate's report, rather than having to undo it or rework some other way.
I understand that Bert Harris is likely to be opened up again next year - maybe this is a fix that everyone could agree on as a way to limit the cost and expense of litigating over these matters and provide a second chance for a local government to hear a contested issue after the real issues leading to a denial are more thoroughly explored.