[wrxtasy]

Just confirming, that the Core is directly connected to your TV or Projector and not going thru a HDMI switch ?
Something is interfering with correct HDMI detection.
Tried all HDMI ports on the TV ?

And answers to these question briefly please ?

This could possibly work for you: (Note the Kodi GUI will be pretty slow, as you have probably found out)
Set the Android GUI to 60Hz or best resolution.
Automatic refresh rate On

Now find the Android Refresh Rate Switch App > and highlight Kodi
What this does is switch you TV to 24p movie Mode before Kodi starts.

Now in Kodi Settings > System > Video > Adjust Display Refresh rate > Start/Stop

With this setting you will be able to play other files not just 23.976fps ones.
Its a workaround but will work until a permanent solution is found.