Checked it all. And, I don't see why it needs to be >1cm. As long as the slack it takes up when tightened leaves space between topcap and steerer. Regardless, the 4-5mm number is with the stem bolts still tight, so I cannot fathom spacing is a problem.

And DOS, I checked the threads on the topcap bolt which look fine. I'm assuming the star nut as well, also because it threads in nicely and stays that way. You sure this could be the issue? And yes, I completely slacked the stem bolts so it moved freely around the steerer.