Skirt is my word, meaning that section that hangs down shielding a lower area, like a woman's skirt. Take a look at the cross section sketch here. By skirt I'm referring to that thin vertical area hanging below the bearing area on the cup and extending down to overlap the crown race. Your headset is a bit different in that there's a shield inserted to narrow the gap between the skirt and the crown race, but the concept is the same.

You need to improvise an alternative, that will close that gap, staying below the bearing area, yet not falling down below the crown race. How you do that depends on the exact design, and where you can trap the O-ring so it stays put.

On some headsets, the easiest way to do this is to trap a disc below and extending out from the crown race by 1/8" or so. Then an O-ring can rest on that, and the shirt can either meet it end on, or hang down to close to the shelf trapping it.

As I said earlier, every headset is different, so the exact solution will call for some improvisation.