Taeverling
Plinker
Ok let me first say that I have never worked on a top break so I'm not sure how different they are than a hand eject model .
I do S&W revolver action work and repairs. While I mostly do modern revolvers I have worked on some that were over a hundred years old.
On modern(last hundred years) S&W revolvers the timing is controlled by the width(thickness) of the hand. S&W and the aftermarket offer "oversized hands" that are used to correct late timing. All these hands are thicker than a stock hand but the same length.
On some guns the hand slot has to widened to fit the oversized hand.
Ok some old school tricks is to heat the hand half way between the tip and pivot point until it is red and very slightly bend the hand. it only takes about .005 to .010 to get what you need depending on how bad (late) the timing is. DO NOT OVERHEAT the tip as it will soften and won't last.
If the gun is just slightly late you can also peen the ratchet teeth and swell them oversize to fix the problem.
Worst case some guns that are shooter grade and don't have collector value and no parts available I have centerpunched the ratchets and really swelled them and then retimed the gun. Ratchet look bad as it has centerpunched marks but the gun is now shootable and the great grandkids can shoot great, great, grandpa's old gun again.
I'm not sure about a break top but I would think the width of hand would control the amount it turns the ratchets just like the modern ones.
Leadeye knows way more about the old stuff than I do but just throwing this out there to think about.
Thanks for the site info, I had never seen that one before. Would the tig weld mess with heat treat? Possibly warp it maybe...https://everygunpart.com/manufacturer/smith_wesson several top break parts guns here....you might get lucky
Option #2 find a micro TiG weld shop and have them build up the surface.....