This is way, way, way overthought.
If the property has a single queue system so that customers are "fed" from the front of a single line, that is the setup. But, if there is no such rope line or other barrier set up, one stands in line for the FD person one believes is likely to become available first. Presuming the latter scheme, when the second FD person opened her station, all OP needed to do was move into that line if that is what he wished. Always worth remembering that the move could turn into a 15-minute wait while that FD person deals with a difficult customer.