Okay, so after some extensive testing and suggestions from Mathworks, this appears to be an issue with the MCR, not the CTF Archive as I had originally thought. Although the Mathworks team has insisted a CTF archive cannot run from a read-only source directory like a DVD, I found that it will in fact do so provided the archive has already been extracted to the same location.
The MCR is another story. The MCR I need to use is hosted on a network location or available on a DVD; it cannot be installed on each and every client machine I want to run the application on for practical reasons. Although the MATLAB Compiler documentation suggests that it should be possible and even simple to run a deployed application using the MCR from a network folder, every attempt I've made to do so has failed. It is as if the application can see the MCR and read the files, but something critical is missing. And of course, the only error it generates is the useless mclFreeStackTrace popup.
So, if anyone has any idea what might be going on here, I'd love to hear it!