If you want patterns at 55-60 yards you are going to have to shoot something with more pellets in it than #4 shot.
I agree. It's been a rare shotgun of any type that I have seen with my own eyesthat firedwhat I would call a good killing pattern at 50 yards with lead number 4 shot. But the problem with a 10 gauge is that most of the shells being loaded for it by factories out there seem to be geared towards geese or ducks. There are not a lot of loads out there in shot sizes smaller than 4. The rise in popularity of the 3 1/2 inch 12 gauge super mag has not helped improve the 10 gauge ammo situation either. Winchester does load number 5 shot intheir Supreme turkey line of shellsfor the 10 gauge and at 15 bucks a box that would be the cheapest thing to try. Federal also used to load number 5's in 10 gauge in their Grand Slam Turkey line if you can still find them. It should improve your patterns some just by the increased number of pellets and number 5's will kill them just as dead. I would recommend an after market choke as well.
IL-Cornfed recommened an Indian Creek and I agree they are one of the best. Problem is that I'm not sure they make a choke for a 10 gauge. The Jellyhead is usually a pretty good choke in a lower price range. For a little more money I think Pure Gold makes a 10 gauge Browning turkey choke and their chokes are excellent.