If you aren't looking for a new receiver or TV, how about stripping the audio off of the HDMI connection before you pass it on to the TV?
This Blackbird™ 4K HDMI® Audio Extractor extracts the audio signals from HDMI video streams. It supports analog stereo audio, as well as high‑definition multichannel audio st
www.monoprice.com
Hopefully your Bose system has at least two digital audio inputs to support a world that has more than one audio source. If not, you will need to switch cables around or get another device to handle that.
Once you start spending more than about $50 or $100 solving this, then your issue is with having the wrong equipment for your needs.
But, people seem to forget or not realize that you can use HDMI audio extractors to get either analog audio or optical audio off of HDMI without much issue.
