In the OP's case there wouldn't be 1500 other people as it's an international flight to South Africa. As far as I could tell, most international flights, even to South Africa, were still flying, just on altered routes.
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As for service desks, just because it's NGCI-equipped doesn't mean there aren't counters available to non-status pax, there are, it's just a long line. Though as noted by Taezar, fronting up to ground staff by a kiosk would probably be the simplest fix.
Oh and of course, what do statistics say about 1500 people all accidentally clicking "Yes" to a dangerous goods question at OLCI at the airport at the same time?