Try Hevi Shot in either the magnum blend or the 6's.
This. Not cheap, but! By the time you buy 4 or 5 brands of standard lead shot you could have easily just gotten some Hevi-13 in either 6's, 7's or mag blends. Through that Jellyhead it will out pattern lead by a margin that would be considered a route in a football game.
Shoot at a full sized sheet of paper like poster paper or craft paper. It's the only way you can see what your whole pattern is doing and where your shotgun is throwing the center of the pattern. Trust me, many, many shotguns do not throw the center of their patterns perfectly in line with the bead down the barrel. It may take an adjustable sight to get you perfectly on target.
To fairly evaluate each shell you should clean your barrel a bit in between shots. You will see a drop in pellet count as your barrel starts to foul with plastic from the wads and residue from the prior shots. Not a major cleaning but one of those bore snakes pulled through the barrel a few times will suffice. A really thorough cleaning after the patterning session is recommended however. If you really want to get serious you can polish the inside of the barrel (as long as it's not chrome lined like a Benelli don't worry Remington's aren't) using a method you can easily look up on line.
With Hevi-13 from that gun you should easily be putting around 150 pellets inside a ten inch circle at 40 yards with the straight 6's; around 180 inside ten inches with the Mag Blend 5x6x7 duplex loads and well over 200 with the straight 7's. And yes the straight 7 hevi-13's will kill like cyanide to 40 yards.
Good luck and good shooting.