Update ...
The Redding carbide expander ball arrived yesterday. I promptly installed it and tried it on a few more once-fired cases.
While it pulled through the neck with noticeable ease compared to the regular ball, it still pulled the cases crooked, with about .004"-.005" average runout at the case mouth.
I switched over to resize some .30-06 cases, and the .30 cal. ball is still easier to pull through than the 7mm carbide ball.
I've got to think it's something about the die body now. Anyone?