Have somewhat similar problem that started after a starter bendix change. At times, numerous times the bendix will not go into the flywheel or mesh when attempting to start. You have to turn the key to start a few times, during which you hear the bendix slap the flexplate but not engage because it didn't mesh.
I have shimmed, shimmed, shimmed until..... I have had the bendix changed again, used all parts of another starter, but bendix.
Checked the flywheel with all seeming to be OK?? Missing something. Any thoughts?
Note: I attempted to knive the edge of the bendix to remove any flat spots on the outer edge and it seemed to help some. But still not solving problem.