Personally, I wouldn't feed any percussion guns really big loads. Flint guns on the other hand have a vent hole to release some of the pressure. Also when I have suggested big loads in the past these loads were intended for flint guns with large breeches, and well made stocks where the breeches are fitted well to the wood and the grain in the wrist is excellent. I suppose 20 bores ought to have at least 1 1/8" breech and 12 and 10 bores ought to go at least 1 1/4" or more.
2 oz is probably too much for a 20 bore, it probably wouldn't be any more effective than 1 5/8oz or 1 1/2oz. The pattern board would tell the truth. A 16 bore or a 14 bore could probably handle up to 1 3/4oz, maybe 1 7/8os , 12 bores should handle 2oz - 2 1/4. 11 and 10 bores should handle up to 2 5/8. Most all of this info comes from a good customer of mine that was an avid turkey hunter who hunted in eight states every year. His 10 bore loads were used in a flint gun with a 50" barrel, lots of jug, 140gr 2ff and buffered nickle plated shot. His results were quite impressive. I probably built him six or seven turkey guns over the years. I did some preliminary patterning per his advice before I shipped most of them. His loads would definitely get your attention. One 20 bore I built him put all of the 1 1/4oz load of #4's in an 18" circle @ 25 yards. The recoil on that particular gun wasn't bad at all.
Anything over 1 5/8oz will create some noticeable recoil, the biggest loads will really snap your head back, that's why I suggest well made guns with excellent grain flow and big barrels. Most of the big turkey guns I have built weigh in the 8-9 1/2lbs range due mostly to the weight of the barrel due to the size of the breech. A buttplate at least 2" wide and 5"-5 1/2" tall is helpfull too.
If you're scared of the bigger loads try 1F, it gives a little softer punch on the butt end.
Let me add, for most applications I wouldn't recommend these large loads, they have a specific purpose. They are for guns with alot of jug choke and killing turks at long distance. I imagine they would be quite effective on wildfowl as well.
For upland hunting I'd use a gun with light jug and would load a "normal" size load. I hunted with a 12 bore flint for years loaded with 1 1/8oz for pheasants over dogs. Might have bumped that load up a bit with out dogs. I had a SXS 18 bore that I loaded 1 oz in. Got a couple pheasants with that load and discovered the gun shot 7/8oz just as well and was easier on me and the old gun, in fact I shot quite a few birds with 3/4oz. That gun would turn skeet to dust with 5/8oz loads. So, big loads aren't always needed to get the job done.