Wait... will it?
I always thought all current spawns poofed and there was a random server-side re-roll for what that spawn gets repopulated with. Might be the same mob, might be a different one. Does it save the current state of spawns and reinitialize them all when it reboots?
If that's the case, if I fought my way into a zone and the server goes down, will all the empty spawns between me and the exit then be filled up when the server comes back online, or will they still take time to pop again?
Whatever the case, I do sympathize with the idea of trying to kill the named before the server goes down if you see it. It's not like you can log in again in 5 minutes. It could be a long time before the server even comes up again, and in that time you may or may not IRL be able to hang around for that to happen. If you come back the next day and someone else has come by in that time and popped the pop, you're out of luck. Get it while the getting's good, imo.
Oh: and here's a theoretical solution. Is there a command to boot someone off the server who is currently online? If so, could you make a macro so when you run it: A message is server-wide broadcast about things coming down in 5 minutes AND a timer is set up for 5 minutes AND when the timer runs out the macro auto-boots everyone off the server? (and maybe even the macro can then lock the server too if needed?) Then it wouldn't be someone busy who has to do it - someone just has to run one macro, and everyone can give it 5, 10, 30 minutes or however long they need to actually take it down on their own time at their own pace, and all the players all get booted off exactly when they expect it.
Just a random suggestion that might be helpful.