Rich,
I have a couple Hardinge lathes, including a BK. Fortunately, mine has a good cross slide screw and nut, but I would not be intimidated about making a new one. Only two operations would be challenging: threading the screw and tapping the nut. There are ways to do both, though, with a bit of care.
First, I would look for someone who has the nut tap and bushing. These were supplied at one time by Hardinge since the nut is designed to be drilled, reamed and tapped in-situ after the cross slide is fully aligned and scraped in. This assures alignment of the nut and screw. The full set of Hardinge drill, reamer, tap and associated bushings may not all be necessary. But having the tap would be very helpful. Likely, another group member may have one that could be borrowed.
Once you have the tap, you can use it to measure from to turn the threaded portion of the screw. If the unthreaded portion of your present screw is in good shape, you can cut off the threaded portion and attach a suitable piece of barstock and thread to match the nut. That saves lots of work reproduding the finicky aspects of the rest of the shaft, particularly the gear. Several methods of firmly affixing an addition to the shaft would work, including siver braze, loctite or boring and threading.
I have done this on my Hardinge TL lathe (identical cross slide screw design to the HLV) with good success. I bored the sawn off end of the screw about 3/8" and turned a matching spigot on the mating end of the new piece. I allowed sufficient clearance to get good braze metal flow into the full length of the bore.
Regards,
Jim S.