"Right ... Well, you see, we were prepared for people who canceled their
participation, but since those people paid with their money upfront, we can't
really accept new participants."
For this kind of party, normally people would make a list of participants in
advance and give those people on the list their invitations. This was to prevent
outsiders from entering the party without permission.
Even if I were to insist on paying now, since the list was already made, it
seemed like it would be impossible for me to apply since that meant they
would need to update the list.