Finally... success!
While I wasn't able to get the current PiCore 7 stable release to work with the camera on my zero, I was able to get the latest PiCore 8 release candidate and add the rpi-vc.tcz package from the 7 repo. After doing this, vcgencmd get_camera reports supported=1 detected=1! And alas raspistill takes a picture!
I've only been using the PiCore RC 8 for a short time, but it appears to be stable. My RT8188CUS wifi dongle is working well with the rtl firmware package.
Thanks again to the TC team. Tiny core is awesome!