registration is free , easy and welcomed !!!
Open the choke up or go to smaller shot. x2 The best pattern I've seen with a 1300 have been either with a IC .660 or a PG .670 using HS 3-2-7. Both chokes cosistantly averaged between 240 and 260 in a 10" circle. It seems you like #6 HS, so I would open the choke up a little. Hevi Shot deos not need to be constricted like lead to get a good hunting pattern out to 40 yards.
Big paper
What about the hevi shot choke? It's ed is .662