The black screw is the one that holds the horseshoe PCBs to the inner posts on the plastic part. It's too small for a 7/64" hole and too large for a 3/32" hole.
Since it's between 0.093" and 0.109", it is probably a #3 x 5/16". (0.099" diameter threads)
If so, those two screw holes
probably should be enlarged from about 0.055" and 0.070" to about 0.081" (#46 drill bit)
or 0.078" (5/64" drill bit) to reduce the odds of splitting.
The larger bolt screws perfectly into a 1/8" hole, and slides through the larger holes on the end of the plastic part. Note that it just passes through that hole, it doesn't actually screw into it.
From your pictures, it appears that the machine screw is #5-40 x 5/8". (0.125" diameter threads)
For these holes, a *very* slightly larger diameter hole will allow the screw to pass through easier
or you can run a 1/8" drill bit through them.
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Do you have calipers to verify the outer diameter thread sizes?
Scott