Again....If you're using the TV's internal tuner for TV reception (antenna), set to DD (or both DD/PCM) and connect to AVR.Turntable.... non issueLeave HDMI from XBox to TV and run optical from Xbox to AVR for DD.There's no need to buy a new AVR IMO.
Or... connect whatever external devices you are using to the HK AVR using optical or coax.
Use the optical out from the TV only if you are using the TV's internal tuner (and set to DD).
Depending on what you are connecting:
HDMI "in" to the AVR from external sources.
HDMI "out" from AVR to TV.
Optical or coax from external sources to AVR.
More info would help for specific suggestions/recommendations.