Just remember that, as an example, Melbourne IT has probably two orders of magnitude more clients than you. A 24x7 pager service would attract a /lot/ of "Emergencies" and as such they'd have to consider running at least a muppet level call service outside of hours to filter "emergency" requests away from the normal signup procedures and over to the People Who Really Fix Things.
Of course it's unreasonable to expect a registrar to have to put up with such a burden during off hours: God only knows what kind of silly calls would come in. "Emergencies" are best handled in a batch during the regular work week. For the stuff that really won't wait, you just put a lawyer on retainer, who can fax off a letter telling the complainant to sod off until Monday morning, or until the moon is in the seventh house and Jupiter aligns with Mars, whichever comes first. I mean, if we can't be on the golf course by 3:00, what are we in this business for, anyway -- right? Jim Shankland