I apologize. I really did try my best to include all information about the project, but I still missed that detail.
I do have more information though. In the .iso, under /boot the core.gz is a different file size than the standard build. That, I think, is expected because that is where the packed files are stored. Examining it with 7zip however, shows a "Data error in 'boot\core.gz'. File is broken" error.
Edit: There's more...
With the working version that I remastered to have bash and nano, there is only a boot/core.gz/core file, but with the build downloaded from the site (TinyCore-current) there is /boot/core.gz/core.cpio with all the /bin /dev /etc /opt (etc) directories that you would expect.