Since no one is replying, let me take a shot myself.
(I'm rather sure there is a write protect somewhere in or around the camera flex, or is the flex itself.)
The procedure for installing ChromiumOS would go more or less as follows, errors due to my gaps in understanding guaranteed: First, you would need to flash a different EC ROM, as I'm sure, or know, from reading the current EC ROM's code that it's at least partially tailored towards Android. In order to do so you would need to disable the write protect indeed, or modify the GBB flags, but you can only modify those when the write protect is off.
Of course my ryu has fastboot unlocked, but unlocking fastboot only serves the purpose for Android and is not full dev mode on the Pixel C.
Checking the output of "ectool switches", we see that the WP is enabled:
dragon:/su/xbin # ./ectool --interface=dev switches
Current switches: 0x00
Lid switch: CLOSED
Power button: UP
Write protect: ENABLED
Dedicated recovery: DISABLED
Once you have the WP off, you can flash the proper EC, which I'm sure exists somewhere at Google but is not readily available in chromium git (either not at all or one would have to do some serious digging).
If you have that working, you could probably piece together a ChromiumOS build for ryu. Then you'd need to repartition the storage. Next step would be flashing the build, and here it's really speculative.
Assuming that the recovery mode is fully functional, one would only need to put the build onto an USB drive, and assuming the Pixel C is in host mode while in recovery, attach the drive to the USB-C port (either directly or via some kind of adapter or somesuch).
From there on out, if the firmware is properly prepared, it should (could? might?) install the ChromiumOS build and would then be capable of booting it.
There are so many ifs and whens though that unless someone from Google backs us up here we'll probably lose a bunch of ryus until we get this working properly. I mean, who wants to pry off their screen to disable the WP?
(PS: An alternate solution would be a Chromium EC ROM that is signed by Google. But alas....)
Milosz