I had this very same problem this morning: all of the sudden, I started getting the KGCore Plugin error message.
Final Cut wouldn’t open at all, so there wasn’t any question of cutting and pasting to a new project to try to work around the problem — and I’m not sure that would solve the problem anyway.
I spoke with Apple, and searched around, and it seems that the only way to solve the problem is to do a clean re-install of Final Cut Studio.
Before doing so, make sure you remove Final Cut Studio. Also follow the instructions for removing Compressor and related files at https://support.apple.com/kb/TS1888?viewlocale=en_US
Then reinstall Final Cut Studio. You will lose your settings and preferences, but the good news is you will be able to work again.
Good luck!