Your local courthouse may not even do jury trials. It doesn't do the sort of cases that require 3AM emergency warrants. If it's that important it can go in front of a district or federal judge, otherwise it can wait for business hours.
Local police departments don't need the ability to engage a global surveillance apperatus at the drop of a hat. Stuff like that can be ran up the chain first.
Who would you even give the data to if they are closed? Fax it over the the courthouse if you are concerned, or tell them it's at your location ready for pickup. If they are legit that won't be a problem.
The data is collected by the LEO, not the court. But yes, you can fax it to the law enforcement office, whose number should also be independently verifiable.
Can you point us to an incident where this has ever happened, namely, where a service provider didn't to respond to a demand immediately while they verified its authenticity and someone went to jail for it? Or even got a finger wagged at them by a judge? Third-party records production is almost never time-sensitive to the degree that, say, a warrant to search for drugs or contraband is, and there's little risk of spoliation of evidence.
You cannot conclude that because someone has been held in contempt for intentionally failing to respond to a records production request because they simply didn’t want to do it, that someone would also be held in contempt for delaying production for a few hours while they make a good-faith attempt to verify the authenticity of a request. Judges take all the facts and circumstances into account—including intent—when making these kinds of decisions, especially those that involve depriving someone of their liberty.
Local police departments don't need the ability to engage a global surveillance apperatus at the drop of a hat. Stuff like that can be ran up the chain first.