[noggin]

The Shield cannot run LibreELEC and never will

Pardon my ignorance.. but why? I've seen some people at least attempted to run regular linux on the shield ( here is an example ) even tho I do recognize no widespread distro runs natively on it without some serious hacking)
So currently the only way is to have the shield run Kodi is is using it's native Android OS and install the Kodi APK on it? 

The issue with the Shield TV is the lack of Linux Tegra X1 video decode support AIUI. Last time I checked there were no nVidia Linux drivers for their X1 that supported hardware video decode in a manner that would work with Kodi.  Without those, you have no hope of a Linux Kodi solution that approaches that of the Android quality on the X1.