Well, I'm not getting anywhere with that tactic.

But at least I know what I'm dealing with now. What I thought was a broken spacer is the compression ring, the split is seen here.
It's plastic, so shouldn't be binding chemically with the steel steerer. I sprayed in some lubricant anyway.

I tried hammering the tube down, and tapping metal ring below the compression ring, no movement in any case.

The ring must be a write off by now, so I guess I'll just dig it out with a small screwdriver.
I just hope I can find a replacement.
I'm not in the US, ordering parts online is difficult. Local shops have either cheap crap or really expensive racing gear, not much in between.