While I had the tooling plate off, I cleaned the crud out of the tapped holes and ran a handful of 1/4 inch stainless steel 10-32 setscrews just below the surface:
They’re pretty much invisible, of course, but they’re all present. FWIW, you need a 3/32 inch hex wrench for 10-32 setscrews.
In the event that I gouge the aluminum surface (you can see the odd ding and blind hole) through a setscrew, I’ll regret doing this. Not having to remove the plate to dig swarf out of the last clamping hole after carefully aligning a part seems like a win.
The Smell of Molten Projects in the Morning 
While Sherline considers the tooling plate a replaceable part, it would still be $60 and inconvenience to replace it. While you could make or buy brass or other softer metal set screws, I doubt it would be worth the trouble.
That would certainly be gilding gold in this situation.
I know I’ll eventually chew up a screw and probably destroy the cutter in the process. Will that knowledge provide enough motivation to remove every screw that could get chewed up, before starting the cut, so as to prevent the problem?
Naaaah…