Kroll,
With a sixteenth inch of movement, if it were all attributable to the nut, you would have virtually no threads left as the thread thickness can't be much more than that. Have you adjusted the cross-feed screw end float? You do that by differential adjustments of the nut that secures the crank and the nut between the crank and the dial. Best done with the carriage nut run off the end of the screw at the rear. And it will be easier to do if you have a thin pattern (tappet) open-end wrench for the nut between the crank and dial, and a box end for the crank nut.
If you do replace the cross feed brass nut, also order a couple of 9-87 Washer, Carriage Slide Nut. These are actually shims. The original illustrated parts lists show it as one round washer, but they are actually rectangular shims. I think that the copy of the parts lists in Downloads have been corrected but if the washer still shows as round, let me know.
Anyway, to properly install the nut, first adjust the screw end float to minimum. Then install the new nut but only run the round head screw down to finger tight. Pull back on the cross slide and start turning the crank until the screw engages the nut, and then retract the carriage until the nut again runs off the screw. Push the carriage and turn the crank until the threads grab, and then about 8 more revolutions of the crank. Loosen the round head screw slightly and then with your fingers carefully tighten it until it just touches the top of the cross slide. Note the position of the slot. With a screwdriver, fully tighten the screw, noting how may turns or fractions of turns the screw makes. The screw is 20 TPI which is 0.050" per turn. Calculate the shim thickness required from this and the number of turns and fractions of turns. Crank the nut back off of the screw, install the shims (if needed), back the nut fully onto the cross feed screw, and fully tighten the round head screw.