Without knowing much about your gun, I think your problem is more that your gun won't cycle low brass 2 3/4 shells. A lot of semi-autos will have trouble ejecting that type of shell. Especially if your gun is chambered for 3 1/2 shells. You should check the paperwork that came with the gun. Some guns have adjustments you can make to allow it to cycle weaker 2 3/4 shells. For instance a spring loaded semi sometimes has an extra ring you take out. Hope that helps. Experimenting with different ammos I don't think is the answer, they all have the same amount of powder really. Unless you jump up to a high brass shell, but then we are talking price as well.
I agree with Jim and Bill. Sounds like a gun issue. But another question would be are you doing it as a sport/compition or to keep your shooting skills up to snuff? If you are doing it for fun and to keep you skills sharp then I would suggest that you stay with the shells you use for your feathered flyers (assuming lead shot). The difference in shot speeds and patterns could make a big difference in the field! I used to compete in skeet (very small and local shoots), but I did really well, but I used what I used for my dove shoots, WIN SuperSpeed (1325fps). Makes a difference when you drop to 1150 (which I think the speed is for them). In addition, they are a little more pricey than other rounds, but they are great, consistent and re-loadable rounds! Hope this helps some.