There is no ZFS package for OpenWrt. So much for "a little side project" eh?
convert the vmlinuz file into a uimage (google this)
try loading it with tftp and see if it's at least starting up the kernel and not stopping just after loading.
find out your onboard flash chip specifications to see if it's using 64k blocks or 128k blocks
Find the partition list of the onboard flash (should be in uboot's "printenv", you can also see something in the boot log in the OP)
7 cmdlinepart partitions found on MTD device nand0
Using command line partition definition
Creating 7 MTD partitions on "nand0":
0x000000000000-0x000000200000 : "safe-k"
0x000000200000-0x000000a00000 : "safe-r"
0x000000a00000-0x000000c00000 : "kernel"
0x000000c00000-0x000001400000 : "rootfs"
0x000001400000-0x000002400000 : "usr"
0x000002400000-0x000002600000 : "data"
0x000002600000-0x000007fc0000 : "app"
since you don't want to touch sources, you probably need to edit the bootcommand in uboot to have a rootfs= variable that points to the /dev/mtd2 or something. Hoping that the pre-compiled kernel is actually receiving the partition table fro the uboot.
If it is not, you need to find where in the source code the partition table is defined, and then edit it to be correct for this device. Yes partition table in embedded devices is usually hard-coded in the kernel, this requires recompile, especially in old stuff like that that is not using dtb (which can be at least compiled separately and bundled with the kernel later).
Then use tftp to send to uboot the root-jffs2-xxxx file with the right block size and write it to the right partition, also send the uimage and write it to kernel partition.
The mere explanation of the steps to follow requires a lot of time and skill. What I told you above may or may not work for you and it's still very generic. You are not installing Ubuntu in a old PC where everything is following standards and the sequence of steps is defined and easy to follow.
You are reverse-engineering how a specific embedded device is built and trying to take over with a different firmware (that also has not been maintained for over 10 years). A lot of what you must do requires trial and error to find out the right combination, and also understanding of how uboot and devices work to guess what COULD work in the first place.