You might consider shaping a single point acme form tool from HSS or silver steel. Use it as a hand chaser with a suitable rest and the leadscrew held in the chuck and supported by a tailstock centre, on lowish speed.

That's how old-timers cut some threads.

Rather difficult to make in tool steel, but there might be another way. With an indexable external threading tool an an 8 ACME insert, the leadscrew could be cleaned up simply by chucking it up in sections with tailstock support, and letting the insert pull the saddle (carriage) along about 8" at a time before re positioning it.

I successfully added 4" of 8 ACME thread to the Tom Senior Xaxis leadscrew to allow fitting backlash adjustable nuts. After cutting the new thread, I had to cut the entire length to match the centre part which had some wear or the antibacklash would not have worked. It was done in several sections with as much tailstock, fixed and travelling steady support as I could manage. That leadscrew was twice the lathe centre length.

Your leadscrew could be deburred in short sections close to the chuck using any suitable lathe tool before running the threading insert along.

If it is only the thread edges that need a little cleaning up, 28 degrees at that edge would make no difference to the operation of the screw. At present it would seem the most likely outcome of using this rough-edged screw would be the early demise of the half-nuts – possibly driving both forwards nd/od in reverse.

I would not be interfering with the face of the threads, if not required.