My youngest son uses his 20-gauge SxS for deer. He does have two different sized projectiles. Each just fits into the barrel since the gun has some choke. It's .626 Right and .610 Left in his gun. He loads 80 grains powder, card wad, bare ball and OS card. Using the 2 beads on the barrel as "sights" he makes a figure 8 and puts the top of the 8 where he wants the balls to land. It is dead-on at 35-yards with one big hole if you shoot a shot from each barrel. A little closer or further distance will still land both barrels shots in an 8" circle or smaller. Since taking a deer with this as a kid, he really likes the bang-flop that happens most of the time or the obvious blood trail other times. He always takes this gun to the ground blind or treestand where we have them set up for 20-30 yard shots. I am not surprised your shotgun performs likewise.
Same gun is a great bird gun. He's patterned and played with components extensively. This gun like 1-ounce of shot (even though its a 20-gauge) and an equal volume of powder from the 1-ounce scoop. It also prefers medium sized shot - 7, 6, 5 patterns best. It also does best with a hard card over the powder and a thin card over the shot. The hard cards are 19-gauge but the OS cards are 20. When we shoot ducks over our pond he switches to 1 1/8 ounce scoop for powder and shot, and #5 Bismuth. Same card wad configuration as the 1-ounce loads. He does as well as the rest of us with 12 or 10 gauge and even modern guns. Same for turkeys although the #5 may be lead.
Funny thing about his shotgun..... If you go down to #8 shot it patterns less effectively than a little bigger shot. If you go up to #4 shot it patterns less effectively than a little smaller shot. And he's tried a lot of cushion wad, felt wad, card wad combos but the simple 19 gauge hard card and 20 gauge OS card always produce the best patterns with 1 - 1 1/8 ounce of shot and equal volume of powder with shot sizes 7, 6 or 5.
You have a very versatile gun! A little experimentation should prove that out. I think you just need to keep messing around with component combinations until you find the right formula.