gprintemps how sure are you that the NUC is rebooting, and it's not actually Kodi crashing and restarting? These are two VERY different failures.
Assuming this is in fact Kodi crashing, then boot the NUC using your USB stick, enter the "live" mode of the installer, allow LibreELEC to start and complete the startup wizard making sure you enable ssh. Connect to the system with ssh (username: root, password: libreelec), mount your internal system disk (usually /dev/sda1, and what would normally be /flash), edit syslinux.cfg (most probably the version in EFI/BOOT) and add "ssh" to the end of the kernel command line (the line that begins "APPEND"). Save the file, then shutdown, remove the USB and boot the system normally.
Connect to the "rebooting" system with ssh (username: root, password: libreelec) then run the following commands:
and paste the two links.