I believe I have the same rifle. The barrels on the older Pedersoli's are an odd size, mine falls between 3/4" and 13/16". If run-out was bad at the muzzle it would be pretty obvious and the OP didn't remark about it. Because of the wall thickness on a .45, the most run-out possible at the breech is 1/8" or less. At 25yds the largest possible change in POI caused by run-out should be around 3.5", plus the drop from the ball and powder combo - which should be minimal at that range. Still along ways from the 18" reported by OP. Makes you wonder what's up with that barrel.
Nice to see the the math. And there's a lot to wonder about since basically everyone has been going on a cloud of assumptions (and descriptions assumed to be accurate) centered around a pretty strange-looking rear sight. But if the barrel has been bent, that should be pretty easy to see with a decent straight-edge, shouldn't it? In fact, by exterior geometric means alone you can determine pretty much everything of interest about the barrel and bore geometry EXCEPT whether the bore is exactly colinear with the barrel -- and with some additional work you could probably come close to determining that. Plus ... how far off colinearity would it have to be to make an 18" difference in impact at that distance? I think Nor'Easter's post here works towards addressing that question.
So I guess my point here is that by purely external geometric means you can tell definitively if the barrel is already bent. If it's NOT bent, AND if the muzzle/crown appears okay (Do we even know this? And how much difference COULD it make?), AND the data we've been provided has been gathered by shooting the gun from a solidly supported bench rest position (to avoid shooter error), AND the sights are in fact as described, THEN about the only thing left is lack of alignment of the bore with the barrel. But again, NorÉaster's post indicates that wouldn't explain the magnitude of the deviance.
But there are things in here that are still assumptions. We've never even seen a picture of the front sight and muzzle (Why is that, since it's been requested several times?), and so far as we know, the only way the rifle has been fired is offhand (Why is that? It's NOT an approach any sane person takes to resolving a problem like this.). Hence my earlier suggestion about Münchausen by Proxy (and if you don't get that at this point, I think you never will
; so let it slide).
How about the hypothesis that the barrel has previously been bent (don't check it, just assume it as a lot of other things have been assumed here) AND the bore also isn't colinear with the barrel. So that allows a narrative that the barrel was originally manufactured with the bore out of line with the barrel, and THAT resulted in someone bending it at some point, and THAT could explain the huge deviance in point of impact. I like that story. It has no empirical support at the moment, but it sort of hangs together. And it provides for a speedy resolution: take the gun to the dump. Life's too short to try to fix that mess.
Problem solved.
