You can do better than that. 3" should be the max. When I had one, I found the first shot always had a different elevation than subsequent shots which grouped together. I've noticed this on more than one semi-auto I've owned.
Try those Winchesters again, but this time, take a first shot after dropping the bolt. Put just one shell in, and let the gun cool, and try another that way. See if they don't group much tighter. I wish it didn't do that, but to me the first shot is the one I want to set the sights to, not that an inch at 100 yards matters much on a deer hunt.
I won our g & f's iron sites standing shooting competition with mine years back. I knew that after the first shot I had to change the elevation by an inch on the subsequent shots and I put a nice pattern around the bullseye. It was so long ago, I've forgotten whether it shot high or low after the first shot.
