I "think" you can't find anything bigger in a 20ga is due to a couple reasons. First off, the 16ga was/is considered a good bird/deer ga way back when they had unprotected shot (no shot cups) and the 16 was very popular. It didn't set the woods on fire, but it worked up close. .410 buckshot has always been more or less for 2 legged protection or rabid dogs ( about the same thing,right?) The 20ga became popular about the time shot cups.modern powders,etc came along and #3 (later #2) was the largest thaqt could pattern well out of that bore size. It's like when the 3" 12 came along, #1 was a far better overall killer than 00 because it patterned better. Nowadays, with even more modern components/loading methods a 3" 12 is Beast of Wrath on about anything, ha. I dare say more money was spent on developing great slug rounds for a 20 than buckshot. Up close, #3 can kill just about anything, but you can't use it. Unless you just want to experiment ( not that there's anything wrong with that,ha) you'd be better off with a good 1oz 20ga slug or a bigger gun.
Now, if you "really" want to experiment, try patterning "ringed" shells....which will be just like shooting a slug in effect. Ringing is cutting the case strategically so that the entire shot/wad/case go out the bore! Not the modern way, but during the Great Depression, people came up with ingenius ideas. They will kill the biggest Brahma Bull in the woods, ha. Myself, I never tried it, I'm not that desperate...but its good to know these things if "if our own Little Depression grows up!