Also, barrel/cylinder gap should be adjusted by moving the barrel relative to the frame, not by shimming the cylinder. As noted, the cylinder should have very little endshake.
I failed to mention that the shim was just to determine functional minimums, once that's determined there are two ways to make it permanent I think.
The barrel threads look to be 20 TPI, or .050" per revolution. One revolution being needed at the least to line up the sights again that means machining the rear end of the barrel to the established gap requirement (After the .050" move back I mean). Then that produces other possible problems with other things attached to the barrel. Still it may be the option, and baring extreme difficulties it's the correct option.
However, since the cylinder (Again, I still haven't measured the gap) may only need to move forward .005" that may not impair functions of the hand and lock bar. To do that permanently I may be able to drill/bore the center hole out to the diameter of the thrust shoulder and maybe .300" deep and make a hardened steel bushing and press that in place, essentially making a new thrust shoulder that sticks out .005" farther out.
That eliminates the problems with the barrel accessories
if I can see that there will be any.
Moving the cylinder forward .005", just thicker than a piece of paper, should not effect the function of the hand or lock.
So, the answer to maximum barrel gap depends. I only have one other revolver to check it against, a model 1858 Army reproduction.
Thanks for the responses, it made me think more about this, and I may decide it's not worth the effort.