Blazed, thanks for the info and picture!
I ended up using a pull saw and it worked pretty well. I sawed off the bottom edge with two shallow angle cuts, then was able to cleanly split the case up along its sides to pull it apart wide enough to slide the coin (and its plastic ring) out. What's especially nice is that it left the remaining part of the slab in one piece and the top labels totally sealed and undisturbed.
Just out of curiosity, why did you crack open that MS-64 error coin (the one pictured)?