I've played around with the pin-between-the-rims trick on one of my guns. I'm not sure it would break the pin on my gun, because the pin doesn't lean against the cylinder. That would depend entirely on the exact dimensions of the gun in question, of course.
However, what I found was that it is VERY easy to nudge the hammer into 1/4 cock, and in 1/4 cock, the cylinder spins freely from that "between the rims" position to the nearest charge hole, where it will lock. Then you are back to carrying 6 in the really dangerous way.
I didn't feel that the "between the rims" method provided enough safety for my taste. A quick nudge, like that which might happen in the very situation that led to you dropping the gun, and the hammer is over a loaded charge hole.
Now WRT whether to screw with a 3-screw, I'm more of the "leave it alone" school of thought. New Models are readily available and relatively cheap either new or used, so if you need a carry single action, just get a New Model and be done with it.
The Old Models are perfectly safe to play with, if you understand the limitations of an original-style single action.