I believe your gun is shooting exceptionally tight w/ the 2 3/4" loads, and the 3" loads are performing more like the norm.
That mirrors my experience, as well. In my cyl bore 870 Talo the Remington 2 3/4" 00 buck patterned better than any other brand I tried (Win X, Federal, S&P, Wolf, others). The plain jane Wally World humble Remington 15 count box beat everything else out. I was keeping all nine pellets in a 30" circle out to 32 yards. Nice.
Then I tried the 3" magnum from Remington (15 pellets) ion the same gun and the results were spectacularly abysmal.
That said, however, the energy released by that big round was stunning. Every shot I took with it the 3" round knocked the entire prop'd pallet over and I'd have to walk in and reset it back up. So sure, the pattern was at least 50% bigger than the 2 3/4". But that stuff knocked the crap out of the target, and there might be a use for that big spread and heavy hit. So I keep some around.
Again, it's not that the 3" round is so very bad. But rather the 2 3/4" buck is so much better (pattern wise) than everything else out there in a general purpose round (not counting the LE rounds like Fed flite control stuff.).