I have a pedersoli 12 ga. and use 35 mm shot cups from ballistic products. Holds 11/4 oz. of heavishot #6. Took a 24 lb gobbler with 11" beard last year at 36 yds.
I use carlsons choke tubes.
In your case the cups will help some-hevishot will help patterns also.
I also use 81 grains of Black MZ from Alliant powder. That equals 89 gr. which is max for my gun.
With this combination I also use Lubed Muzzleloading Shotgun Wool Wads over the powder(1-2) and 1 wad over the shot.
Be careful to not seat the shot column too hard-for me seems to open the pattern.
I also shoot a TC 12 ga. ml with the same components just a larger shotcup and 110 gr of black mz.
try 2 overpowder wads vs. 1 to see what difference it is in your gun.
Hevi shot can be gotten at
https://www.midsouthshooterssupply.com/search?SearchTerm=Hevi-Shot+Bulk or Ballistics products.
have fun.