I don't think they are trying to run down the clock. It sure seems that way, but I hope your wrong!
I sure hope you're right that they aren't trying to run down the clock. Unfortunately, I know that in emergency matters such as this, all papers are filed simultaneously in all of the courts that are likely to hear appeals at the same time they are filed in the trial court (i.e., the federal district court). Therefore, the Eleventh Circuit panel has had at least two full days to consider the issues and begin drafting an opinion based on the arguments it anticipates that it will receive. The reason they can do that is that parties can't raise new arguments or issues for the first time on appeal. Therefore, whatever was presented to the district court will be what the appellate court has to rule on. Maybe they will surprise me, but in my experience, emergency rulings granting relief are usually issued very promptly.