An update: I found out how to extract a NAND backup, so I extracted the root partition from my Cacko 1.23 NAND backup which is an initial setup without modifications.
Then I used the killJazz kernel for Akita as the zImage in the /boot directory, and created a kernel-cmdline by copying the output of /proc/cmdline (but replacing /dev/mtdblock2 with /dev/mmcblk0p3, which is the partition where the cacko root filesystem is in my installation.) I also created the nfo file.
I booted up, and kexecboot picked up cacko and showed it as an option. I selected it, and then the cacko kernel started to boot. Things looked OK, but in the end I got a kernel panic (init not found.)
I tried different kernel-cmdline combinations, but none of the ones I have tried have made things any different, and I'm out of ideas.
I don't know how the kernel looks for initd. If its location is hardcoded in the kernel, then I suppose we are out of luck with this approach, since copying the root filesystem to the new partition must have necessarily changed the memory layout. (Side note: I was investigating also about using dd to make an exact duplicate of the /dev/mtdblock2 partition in my cacko installation as well, but I don't know how to (first of all) create an empty partition which is an exact duplicate as far as block size and so forth.) I have the feeling my newbie status with this stuff is probably not helping me.
If anybody has any ideas it would be great. I might start a new thread sometime soon with a report of my progress, and maybe someone more experienced can give this the last touches to get it completely working.