We had this problem. I replaced the set screw with a socket head cap screw. I turned the screw length so it protruded enough to engage the keyway but not bottom out and the tip diameter to fit the R8 keyway, With a head on the screw, it now is impossible to have the tip protrude too far. The Grizzly mill that I worked on had sufficient clearance to clear the head of the screw but check to make sure on your machine. If clearance ius a problem, there are low profile screws and hex socket button head screws that may work.
To determine the length, I inserted a collet and tightened the screw until it contacted the collet and backed the screw off one full turn. Then I removed the collet and tightened the screw, counting the turns necessary to do that. By knowing the screw pitch and number of turns, you can calculate the the distance between the head of the screw and the shoulder. add about .060" for the protruding tip and .0155" should work for the diameter. The finished screw can then be tightened to contact the spindle which will prevent it from loosening in use.