Thank you for sharing this. At some point in time I would like to tackle sound. I got a Sankyo model Sound-500 projector that is not working, and was looking for info and found the service manual for the Sound-600 model and it has the schematic. Here it is in case is useful.
Hard to say, it may be a coil. If you can get your hands on a multimeter, it should be easy to confirm is not a diode.
But from the circuit, it looks like you have audio at the output of C4, the circuit to the left of C4 looks like an amplifier with some filtering that includes the unknown part.
I am not familiar with the TA7668, but looks like it would do the trick. The board you show has also an amplifier, there are other board that are only the TA7668.
This post shows the use of a modified tape deck with a sound film head.