My expereince with the Kodiak makes be believe that the AP pids are unstable, and hence the inability, sometimes, to lock onto the localizer. ( GS is fine)
Unstable Kodiak AP PID
with a better AP PID
Stable Kodiak AP PID
Try this as a temporary Mod, until the Official Kodiak Update.
https://cdn.discordapp.com/attachments/923240743223562270/926571494031646780/z-Kodiak-ai-mod.zip