It seems that Samsung Galaxy S3 (I9300) may see an official CyanogenMod build, after all. Below is a repository with Android M (6, API 23) for the device.
https://github.com/CyanogenMod/android_device_samsung_i9300/commits/cm-13.0
https://github.com/CyanogenMod/android_device_samsung_i9300/commits/cm-13.0