Guy is correct. But you have two issues: Carry Up and Over Travel.
Correcting Cyl Carry Up
The issue is called a lack of "Carry Up". In other words the hand does not carry the cyl far enough to lock up within the normal cycle distance of the hammer travel.
Frankly, based on your assessment and comments, I believe Pat Sweeney's "Gunsmithing Pistols & Revolvers", 2nd Ed.(2004), pp.219-220 is the most sensible, a perfectly good solution, what I would do, what I have done many times, what S&W factory trained smiths have done in similar situations, and also what members on this forum have done successfully after reading this, which is:
Peening the ratchet tooth (or teeth) to correct timing/cyl 'carry up' is so simple, but you're the only one to decide if you can manage it.
Replacing and fitting a new hand may fix your problem and may not, but the hand is not likely needed or at fault. It's the harder part compared to the cyl.
The flat surfaces of the teeth facing you when looking at the rear face of the cyl are where to peen. The tooth at about 3 o'clock is the next to be engaged by the hand (when cyl is closed) to advance the chamber to the right of the one at 12 o'clock, into firing position. The cylinder turns counterclockwise so the hand will engage the 'bottom side' of that tooth. The flat surface facing you is where to peen, on the edge right above the bottom side of the tooth. No need to take the gun apart at all. I lay the gun on a padded surface on its right side, muzzle pointing to the left (I'm right handed) with cyl propped open with a rolled up shop cloth.
If you're worried about force to the yoke and frame, I'm afraid that you're envisioning TOO HARD of a tap. Just a very light peen with a small hammer and punch is all that's needed. The ratchet teeth are not hardened! This takes finesse, not force.
And by laying the gun on a padded surface without restraint as I described, it's allowed to move when the punch is tapped with the hammer mitigating any force to the yoke and frame.
You may not even see the metal deform and it can be enough to solve the problem. One light tap with a small light hammer and flat face punch then close the cylinder and try it. If the cylinder doesn't 'carry up' or even if it does C/U but still has too much 'looseness' when fully cocked, give the tooth another tap. You can do all six teeth, or just others where there's looseness with the chamber in firing position when the hammer is cocked. Rough handling/constant double action rapid fire can accelerate the teeth wear but it did not happen overnight, and now you have another 10 years of shooting before it'll need anything more, depending of course on how much you shoot the gun. If you peen too much and the cylinder carries up too far that puts cocking the hammer in a bind or the bolt 'jumps' out of the cyl notch, not a problem, peen the surface that the hand contacts and push it back.
Also for side-to-side cylinder play, make sure the edges of the cylinder notches are not burred out or the cyl bolt can pop out of the notch. Gentle peening of the notch edges can fix that as well. "Tight lock up" is fine, but can be over emphasized. Recognize the cyl needs some play for the bullet to align the chamber to the forcing cone.
If you have a new hand and are comfortable fitting it, that's fine. But I would not spend money on new parts, because one can easily handle doing this very minor repair.
The hand is made of harder steel than the teeth since it has six times the contacts of each tooth, and lack of proper carry up is a typical result after many rounds of shooting. That's why I would not install a new hand, it already has the advantage and takes more work.
Correcting Cyl Over Travel
A new cyl stop may take more fitting work than just "tuning up" your original stop, including to the front cyl stop shelf.
If you're game to give it a try, you have nothing to lose by fitting your stop and it will give you some experience before you install a new stop.
1.First troubleshoot:
The 1st thing you want to know is if the cyl stop is reaching the bottom of the notch and if it's centered in the notch.
"Paint" the bottom of the cyl notches with a black Sharpie felt pen. Cycle the cyl around several times by dry firing in single or double action. Look for a "footprint" of the cyl stop in the bottom of the notch; it'll be a bright spot in the ink.
If no footprint, the stop needs raising, see STEP 2 below.
If there is a foot print, is it a square 'footprint' in the center bottom of each notch. If not see STEP 1.
STEP 1] If the footprint is off center, the top of the cyl stop is not shaped right and does not allow deepest and full engagement in the notches. Stone the top surface to reshape slightly so the high point of the stop leaves a footprint in the ink at the bottom of the notch. A Dremel tool with polishing wheel is good for this if you have some skill with one. Either can be done w/o disassembling the gun.
If the cyl line (cyl stop track) is off center in the approach ramp (notch lead), that's an indication the stop is not shaped properly.
Once you get the footprint at center in the bottom of the notch, check for over travel. If none, you fixed it.
STEP 2] If no footprint in bottom of notch and/or cyl still free spins do this next:
Remove cyl stop from the gun and stone a little off the surface in front of the actual stop lobe. This will allow higher protrusion of the lobe thru the frame opening. Stone until it leaves a footprint.
http://smith-wessonforum.com/s-w-sm...an-turned-hand-when-closed.html#post139822921
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Photo by armorer951
And then do STEP 1. Once there's a footprint but not in the center of the notch, the stop can not engage the full depth of the notch. And the front-to-back curve of the stop lobe needs re-shaping of the curve to ctr it. This takes very little stoning to change the curve and 'move' the footprint to the ctr.
If there's a round footprint, the stop lobe top surface has a hump from left side to right side and needs flattening with a stone.
Be sure to leave both of the stop lobe edges square, especially the left edge to keep from jumping the notch.
If the side edges of the cyl notches are burred up, 'upset' them back to flush with cyl surface using a flat tip punch that's polished on the tip; use gentle tapping with a very small hammer.
Recheck that the footprint is reaching the bottom of the notch and looks square.
That will do it. Any questions, please just ask.
HONDO44