The form is the bouncer
A registration form is easy to make and easy to distrust. It looks like it is working while names trickle in, and only at the point of no return do you learn the truth: too many, or far too few, with no way the form itself ever told you. The difference between an honest list and a hopeful one is whether the form holds a limit.
So build the form around three decisions, in order. What you ask for, how many you will allow, and when you stop. Ask little enough that people finish it, cap it to a real number, and close it the moment the room is full.