Hi Forum, I wanted to update you all on this topic with a solution. It is possible to get high-quality, lag-free audio to the Model S (and presumably, Model X and Model 3) speaker system!
The only product that I could find that works reliably is the
Vast International HiFi-FMT V-FMT212R RDS HiFi FM transmitter. It is not cheap (around USD$120) but it actually works, which is saying a lot. The product has a power output of up to 200mW and a range of over 150ft. This power is necessary for the Model S since I believe that the frame itself is the antenna, and the cheap $10 stereo jack to FM adapters do not output sufficient power: barely enough to cover 10-15ft. If you use anything less, you will hear a lot of static: I tried nearly half a dozen different products without success.
The V-FMT212R accepts line-level audio via a stereo 3.5mm jack, or USB audio. To use the 3.5mm jack, the device has to be plugged into a power-only source, or has to be connected with a USB power-only cable (data pins removed). If the V-FMT212R detects any kind of USB data connection, it will deactivate the 3.5mm jack. Therefore, it cannot be plugged in to the USB ports of the Model S without a special power-only USB cable.
The USB audio connection works flawlessly with my iPhone using the Lightning to USB 3 camera adapter. There is no lag and games are eminently playable.

Sound quality is also crystal-clear and uncompressed, for FM anyway.
Unfortunately, the Nintendo Switch does not work with the USB chipset in the V-FMT212R. I am still trying to figure out why. Furthermore, the 3.5mm headphone out jack of the Nintendo Switch does not provide the proper impedance for line-level audio. It is possible to hear the Switch when connected via the Switch's 3.5mm headphone out jack, but the volume is quite poor and boosting the volume on the Model S results in significant amplification of background noise.
To get the Switch to work, I tried the
Behringer UCA222 and the
Schiit Fulla 2 DACs, connecting the line outputs of each to the V-FMT212R. These both work great, with a nod to the superior quality and higher resolution of the Fulla 2 (albeit at much greater cost). Sound now plays through my Model S loud and clear, with no lag and virtually no static at the reasonable volume level of 6. The car is now a rolling game-playin' machine!