Perhaps something like a 1/2 hour time limit,  enforced as a loitering offense, could be put in place.  There seem to be PLENTY of other downtown sprawling and snoozing places nearby - the Park Strip, the old Alaska Native Hospital grounds, the hill across from the AKRR station..  
Town Square Park should be kept enjoyable for workers on meal breaks, for shoppers, for persons attending PAC events.. Is an ordinance needed?  If so, let's have one!