Tapered collet holder--can it be fixed?

[LittleWatchShop]

I picked up this with my watch bench purchase.  It was rather rusty.  After removing the rust, I find that it will not fit snugly in a tailstock runner.  Measuring my good collet holder, I get 4.5mm at the widest.  Measuring the one I cleaned up, I get 4.17mm.  Clearly the metal was oxidized and then removed leaving a narrower tapered post.

It is functional otherwise.  Wondering if there is any way to bring this back to life.  One idea would be to plate it and thus layering the necessary 150um or so on to the post.  Sounds sketchy though.

[LittleWatchShop]

I wonder if there is a smaller taper for a different style/type tailstock runner.  Is that possible?

[nickelsilver]

10 minutes ago, LittleWatchShop said:

I wonder if there is a smaller taper for a different style/type tailstock runner.  Is that possible?

There's no particular standard for the taper, different manufacturers definitely used different ones. I believe the closest thing to "standard" was 2 degrees.