I get this from time to time. Maybe the nut isn't round? I have used lapping compound on the threads and run the nut back and forth until it rotates freely. I would probably use ~280 grit for this job. If it's working you'll notice the nut can be advanced further after every so many strokes.

M16-1.5 is the closest metric thread form. Metric threads typically have pointed peaks and rounded troughs. Standard thread forms are pointed on the peak and trough.

Is this the replacement that doesn't fit?

Yes the replacement nut does not fit. Unfortunately we lost track of the original nut.

I don't think the nut will go on far enough to try lapping. After reading this I think running a hone through the nut to flatten the thread might not be a bad idea. That would explain what is happening.

We tried the metric version and actually can get a few turns on the metric.

I hated to spend the $$ but I purchased a thread chaser for the shaft. I will try honing the nut first.

I'd get some thread wires to check the shaft Pitch Ø.
Fowler 52-485-048-.0 29 bux on Amazon. There ae some cheaper.

Some machine shops pride themselves on cutting shaft threads to fit a provided nut real snug.
Mistakenly, in my view.

Fasteners too close to the tightest pitch diameters have no tolerance for errors in thread pitch and runout and etc.

I took a combination approach. Looking at the shaft with a magnifier I could see the bottom of the threads was more or less flat. Did the best I could to measure the actual minor diameter then opened the nut to match with about .002 clearance. Was still tight but at least I could get a few turns on it so I went the lapping route.

Problem solved :)

Thanks everyone!