I have used a microscope at the lowest possible magnification. And I now believe that the screw is 60tpi. Recall that it is 0.0875" in diameter. The holes in the caliper body are 0.093 using a pin gauge. So that's the biggest screw I can use without enlarging the holes.
Now I need to figure out what that thread really is if I want to replace it without major modifications.
I should add that getting that thumb nut off was an ordeal. It wouldn't budge. I cleaned it in my ultrasonic tub. Then I soaked it in penetrating oil. No joy.
So I used a big pliers to hold the screw like a heat sink and heated the thumb screw slightly, then used a small plier to wiggle the nut. It moved! Yes! From thereon I applied lots of penetrating oil and wiggled it back and forth ever so gently about 15 degrees at a crack. With patience, I finally got it off using a tapping sequence. Plus 45, minus 30, plus 45, minus 30. It never did free up till I was all done.
Under the microscope, it looks like an ACME trapezoid thread. Kind of cool to see that so small. But I'd guess it's just deformation and not really ACME.
Any guesses?