I was finally able to replace the running kernel by remounting in read-only mode the root partition of the Kobo and then overwritting it with the uImage (not the zImage):
dd if=uImage of=/dev/mmcblk0 bs=512 seek=2048
I probably got something wrong in my kernel .config since it starts (the blue-green LED pattern blinks two or three times) but fails to complete the boot-up process. In the end it may not matter, since I was finally able to compile the hid.ko module (prerequisite for usbhid.ko), which I thought could not be built as a module and had to be included in the kernel.
I'll open a new thread once the keyboard is working.