There is a lot of Space in a 3" 20 ga hull.
If you want to increase payload, shooting a longer projectile or a heavier one cut open a slug, and look at the amount of space that the wad(s) take up in the hull.
I have made a few joke 12 ga shells with black powder componets, so many grains of green dot, an over the powder card, glitter or confetti, and over the shot card, 1 ounce of shot and another over the shot card and crimp. The glitter looks great at night and there is enough shot to break birds.
But I digress in you can load powder for a 1.25 ounce 3" load and use over the powder cards, and place in a long 1.25 ounce other than lead projectile in a Sabot or have lead rings to lock int othe lands and grooves if you want a longer projectiole, heavier, and better BC than the current loadings.