I've done about a dozen tower shoots around the great lakes. Most, if not all restrict shot size. I have done all the tasks involved, much preferring to pick up with my dogs, where you can stand outside the ring.
I've been in the tower when the nimrods were blasting 4's and 5's directly at the tower. Openly seeking to kill the birds as soon as they cleared the walls. I quit.
This crude, blood thirsty, slob mentality, overly preoccupied with body count, fitting magazine extension, endorsed by the white buffalo crowd, that gets recruited for these shoots generally behave in an obscene fashion. If you are shooting 4 or 5 boxes at the tower birds, you are wasting your ammo, and are routinely attempting to poach adjacent butt's birds. Bad form in all ways.
If you can't cleanly hit a pen raised pheasant at 35 yards with breast side on, bigger shot is just going to hit the guys in the next butt.
I was run off at NOBS because of my detailed descriptions of Americanized tower shoots.
Use 6's at the largest, (7.5's are more than adequate) and shoot only at the birds that fly your way. Try to bring some respect back to the field if you can.