Unclenick, thanks for the tip on Quick Metal, I'll look into it. I heard somewhere that the carbide sizing rings are pressed into a heated (for expansion) die body and the shrinking die body holds the sizing ring in place. Not sure if that's true or not, but the sizing ring that fell out of my die does not appear to want to just drop back in to the die body.
Sorry, dahermit, I couldn't tell you what I did to pop the ring out.
Can't wait for my new die to show up, I have another match coming up in a couple weeks, and I need ammo!