Turns out the counter opens at 13:15. I was there a little after 13:00 and was first in the "ticketing" line. There were about a dozen people already there in the check-in queue. They only have two turnaround flights per day. Arrivals (from LHR) at 13:55 and 17:55 and departures at 16:50 and 20:25.

Why someone would want to arrive at MIA three to four hours before a departure beats me but there were at least 30-40 people who checked in during the 45 minutes I was there with the counter open.