But there is a solution: the website team should get their act together and remove the "first come first served" aspect altogether.
Do you, citizen, want to register? Cool - leave your e-mail and we'll call you. Is the service optional? Then we'll pick at random from the pool of applicants and e-mail them. Is the service mandatory? Then sign up and we'll call you once you reach the top of the queue. Add a quick ID/credit card/whatever check on top (like good concert venues do), regular e-mail updates to let people know they haven't been forgotten, and you're done.
Any second year CS student could write such a system. The difficult part is accepting that the current approach doesn't work and looking for alternatives.