The sideplate is definitely the issue. Very odd, I know. I just happen to have a CZ-27 in my collection and decided to interchange some parts. The one common denominator is the sideplate. With the CZ-27 sideplate in place, everything is great. The part that stinks is that in all of my infinite care, I managed to break off one side of the sideplate screw head. I cannot for the life of me find any in stock (checked Numrich and Marstar).
The seller was gracious enough to offer to take it back and refund, or fix and return (he's a dealer and knows a good gunsmith). I took him up on his offer and will hopefully get a working CZ-24 back.