I've been using SalixOS-live for few days now on my eeepc (on a usb-stick) mainly because I couldn't install it to sd-card (same problem - kernel panic while booting - on all slack based distros) & have to say I really like salixOS.
Hi, glad you like it.
You're kernel panic was probably caused because the Slackware kernel only contains the mmc drivers as modules, i.e. can't make use of them before the root gets mounted, because they are not in the initial kernel image loaded by the bootloader. This problem could most probably be solved by an initrd containing the mmc_core and mmc_block module as created by: mkinitrd -c -m mmc_block:mmc_core
It's not enough I think. Most media card readers are connected through USB, evn if you can't see it, it's often connected like that inside. So the kernel should also have USB support compiled statically or used in an initrd too. You can grab the Salix Live kernel (/boot/vmlinuz on your USB key) which is quite the same as the normal kernel but with USB support compiled statically.