I know that the BS3 (I have the mk3 version also) doesn't support hdmi-arc from it's specifications.I also know that other newer brand panels have hdmi-(e)arc on 1 or more sockets.
If I remember correct you can setup the audio on a LG C9 panel to be re-directed to one of it's hdmi ports So, in that case the the LG would act as some kind of source for the BS3 . The BS3 would be then a substitute for a soundbar.
The advantage you would have is that hdmi could handle lossless audio formats when you compare it with digital coax or optical spdif, which support at it's best DD or DTS.
Is handshake or protocol the keyword in which is missing with the above mentioned setup?