No, I haven't yet received the smoothing broaches, but once I've tried it I'll let you know the result. I'll be going very easy and I'll try not to overdo it. Hopefully it will make the barrel spin more freely around the arbor. CousinsUK doesn't have the barrel and cover as spare part so hopefully I won't be making a mess of it.
I guess as a general rule it is better not to fix it unless it is broken, but in this case I'm just too curious to see what it's going to do.
Oh yes, the scoring is very light but can be distinctly seen at 40X magnification. It's looks like a countersunk ring around the pivot with a width of only a few thousands of a millimeter. Don't know what would be suitable hardwood (?), but I think I can try with pegwood and autosol first considering the scoring is so light.
I would try replacing the cracked jewel, before doing any pivot polishing. Did you use smoothing broaches on the barrel, and what was the result? My advice is not to change anything you can't change back, unless you're absolutely sure you need to.
"Shelter in Place" has me working on a Movado chronograph I picked up some time ago. The case is a Taubert/Borgel and needed the pendant tube repaired. Now with that out of the way I need to cut a new cork gasket and figure out how to squeeze it into the tube (that should be fun).