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I had a great plains doing the same thing for a long time. I found tha tthe rear sight was a little loose as stated before . that cured the problem for me.
 
Just caught this thread. That target does look like a damaged muzzle could be the cause. I had a tiny nick in my crown caused by my shortstarter at a chunk gun match and my shots went all over the map. You could just barely see the nick, but you sure could see it out at 60 yds. Might need to cut behind the coned portion and re-crown.
 
Well if you checked what the other posters mentioned and it didn't help there is one more thing you could check. If there is any gap between the hook on the barrel and the tang this could be the cause of your problem. The barrel and tang must mate without gaps and some filing may to needed to get that. Hold it up to a light from the side and see if you can see any light between the back of the barrel and the tang.

But really I think you just need to shoot it for a while and it will settle down. You could lap the barrel and there is a great post from GreenMountain Boy on this forum about it. It may be something you want to do a search on and read. I just got a drop-in .50 but have not shot it yet but I don't expect it to drive tacks for a hundred shots or so.

Like Roundball said too; if your cutting or blowing patches that can cause some really wild groups. A cut patch (very possible with a new GM barre) will look fine until you inspect it very closely for the cut and it may not cut it every time. If the lands are sharp they will smooth out after a box or two of balls. Those GM's will handle a heavy charge so I doubt that's an issue.
 
Something is loose most likely.
Try joining the hooked breech with a good epoxy like JB weld or Acra-Glas so its locked together.
Then assemble to see if this helps. If not heating to 400 degrees or a little more will release the glue.
Might try bedding the breech with Acra-Glas too.
54 GM should have a 70" twist. This is their standard for 50-54. They will like heavy loads most likely and should not burn patches with the lube is good.
I can shoot 100 gr of FFF from a 50 GM with no damage at all to the patch.
I would shade the front sight or blacken it.
If you have the adjustable rear sight it could be a factor.

Dan
 
try turning the wedge upside down. they need to be in the same way sometimes. i slotted mine and captured it with a pin behind the escutchen
 
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