Thanks again all. I think I got this knocked out this morning. I was surprised how very little it takes to affect percent of engagement. For a reference, I measured from the rear of the TS, at the very bottom, to where the caliper depth probe bottomed out on the MSH. I mean this wasn't terribly precise, but at least it gave me a repeatable test I could do to see if I was making any progress.
After taking the gun mostly apart, I started with a light polish, since I was kinda skeered to fit on it too much. I ended up with a total of three swipes of the file. I started at 73%, and am now at 44%, so I will call that "close enough". I'm sure most of ya'll have done this a lot, but in case anyone else like me is new to this, pictured below is what I used.
Attachment 106417
I also found it helpful to put the numbers in a spreadsheet to make the computations a bit less of a headache.
Attachment 106416