The problem is the ill fitting female spline on the aftermarket handle, not so much the set screw. The new handle should fit very snug on the male spline on the latching mechanism, but it doesn't.
I was told to tightly form aluminum foil around the spline on the door handle mechanism stud before putting the handle on. This is supposed to tighten the fit, prevent the handle from wobbling, thus allowing the set screw to just hold the handle in place and not be subject to the torque of the handle, and thus preventing it from falling off.... FWIW, might give that a try.
