To machine the register on that chuck (if you really want to go there), if you have a piece of hard rod an inch or more in diameter, you could mount it in your 4 jaw chuck with about 2 or 2-1/2” extending out. Mount the three jaw to the rod (register surface facing the tailstock) and adjust the 4 jaw chuck (and possible using some light brass mallet taps) indicating against the register surface until it reads flat. Then you could face off the register surface, reducing its overall length. I would go easy with fairly light passes, even though it is cast iron.
Or you could just use it as-is.