After lots of thought, I've found a good solution to route the TV sound to the Kenwood Head Unit without tearing things apart to add a discrete cable. I have never figured out why Airstream didn't connect them in the first place, but I understand that ground loops can be created when connecting two disparate power systems (one AC and one DC), but it still seems like that could have been overcome without issues.
After some trial and error, I've found a small bluetooth transmitter that can plug into the headphone jack on the back of the TV and broadcast the sound to the bluetooth receiver in the house system. It carries a Bluetooth 4.1 spec, and also has technology to eliminate audio latency that can happen with bluetooth connections. It is an inexpensive addition, and the sound from the house system, though not great, is considerably better than the TV speakers. After trying several devices (not all of which paired successfully with the Kenwood unit), this one has seemed to work the best:
Note: You can connect this to the "TV Headphone" jack, but for some reason AS decided to configure those as mono connections, rather than stereo, which you can get if you use the headphone jack in the back of the TV. Configuring in this manner will shut off the TV speakers, but you really don't want to hear them anyway.