So after your suggestions I figured I'd try some steel wool I had, followed by some metal polish.
I did a small area of the plier head, and it did not leave any discernible scratches, I thought "this is going to work really well". I had a firm grasp and was scrubbing away, thinking about building a soda blaster to get in the little cracks, and the next thing you know I hear "Click".
I look at the handle, and yep, a lock spring had broken.
So as of this morning it's off to Portland, with a few other tools that needed some warranty.
Not a bad thing in itself, what with Leatherman's great warranty service. But, with the broken spring in the handle, it will most likely come back as an ST 300 instead of a Core.
Time to find another project…