Cool. Is the barrel seated tight against the frame, or is it just the barrel rib that makes it look like it's not tight against the frame?

If the barrel will not go around one more complete turn, the usual way to fix is to remove a bit from the barrel shoulder on a lathe and go a full turn around to tighten the barrel against the frame. If you do not ever intend to reinstall the original barrel, there's an easier way: draw file the front face of the frame until the barrel can go around one full revolution and tighten against it.

Even with the barrel pin, if the barrel is not tight, it will turn slightly to the right with shooting because of the rifling twist, and the sight will not be straight up and down.

Which ever way you fix the barrel, you'll have to adjust the barrel to cyl gap by filing the rear end of the barrel and likely shorten the extractor rod just a bit. But both are simple tasks.

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Jim
S&WCA #819