The K1 is an Intel PXA-255 device (based on the Gumstix that was used in the early eink dev kits). A significant amount of the source code mentions "Gumstix" repeatedly, and some of the devices in the dmesg logs are unique to Gumstix devices, so probably just copied from the Gumstix project. I should post some of the data I gleaned from dumping it, to prevent confusion...
I have also downloaded all the source code for all the versions, from amazon, and also all the old kindle firmware versions from archive.org (wayback machine history for amazon firmware update download web page). It is enlightening to examine firmware update differences over time, and between device models...
Though I still need the modules, and I am curious about how to build them. I am currently studying this:
The Linux Kernel Module Programming Guide.