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IMO, the pattern is decided by the barrel and choke, more powder/speed won't change that.
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Wrong, wrong, and more wrong.
If you don't have the needed speeds, then the pattern is going to hot spot center as you have it filling out for your given pattern size. This is the reason that you have to push 410 with 226gr to over 1300fps to get it to pattern correctly.
Note, the sts box of factory ammo that states is 1200, if actualy doing 1350fps isntead. Wins 410 that states it 1200, is doing just over 1300fps as well.
If you have too much speed , then the Patten is going to light center pattern when you get it to outer circle pattern correctly instead.
Since we are dealing with HS hulls and win 209 primers, really easy to come up with a winning load out of the shotgun in 28.
Powder is universal clays, ream your shot bushing so it will drop 336gr (338gr is max limits for NSSA/NSCA) on the money, and the wad is the CB CB5034-28HS (dark red, and not the pink one).
Start the load with 14gr of universal (1140psi) and start increasing the amount of powder until the load chrono's at 1240fps out of her shotgun (will hit it before you make 1200psi).
Once you have the speed correct, then go pattern the gun to come up with the needed choke restriction in the ranges she will be breaking targets to end up with a clean pattern, and no holes in it that you can drive a mac truck through. Forget all about what you think the outer circle should be, but instead use the chokes that she has that it will put down a patten with enough pellets in the give circle during a target strike that it will cleanly break the target. Hence take a target with you to the patterning board, and make sure that when you put a target anywhere in the shot pattern on the board, you have at least 15 pellets that would strike the target. Hence from center of pattern, to the outer fringes, you have a uniform filled out pattern of shot.
If you want to use 20/28 isntead, have come up with some good 28 gauge loads on the same basis (hit the 1240fps mark), but fell short in 20g compared to my loads using universal isntead (1220fps in the 20 gauge, and why I have stuck to universal).