You can see in the shadow in both photos that the serial # pad under the barrel has been removed making the barrel round; likely turned off in a lathe. I wouldn't do it that way, I just reproduced the 2 step notch further back in the barrel pad. Protects the rod from getting bent somewhat.

I agree, a 1/2 rd sight would be period correct and look the best.

How is the cyl loose? Front to back end play? There's shims made for that. If it's loose side to side, 'stretching' the hand or an oversize cyl bolt fitted. Or much more easily, just peening the ratchet teeth will tighten it up.

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Jim
S&WCA #819