IMO, you haven't found the right load for that choke. You will surely kill a bird out to 30 with that set-up, but you should be able to take one at 35-40 effectively with the right set-up. I know you don't want to hear this, but you might want to invest in another choke. I used to shoot my fathers gun that had a Hastings choke. It was just a Winchester 1300 3" gun and I've taken birds just over 40 yards without a problem. Try shooting the Federal Flight Control out of your current setup. I shot them last year and found they added about 7 yards to my effective range.

Edit: Just realized that you were shooting hevi-shot. Is that choke hevi-shot friendly. That may be part of your problem.