Best method for sending data over a mono audio channel
I think RQDQ has the right idea.  The best method of sending digital data over restricted bandwidth audio lines is a problem that has already been solved for modems.

The 300 bit/s modems used audio frequency-shift keying to send data. In this system the stream of 1s and 0s in computer data is translated into sounds which can be easily sent on the phone lines. In the Bell 103 system the originating modem sends 0s by playing a 1,070 Hz tone, and 1s at 1,270 Hz, with the answering modem putting its 0s on 2,025 Hz and 1s on 2,225 Hz. These frequencies were chosen carefully, they are in the range that suffer minimum distortion on the phone system, and also are not harmonics of each other.
In the 1,200 bit/s and faster systems, phase-shift keying was used. In this system the two tones for any one side of the connection are sent at the similar frequencies as in the 300 bit/s systems, but slightly out of phase. ...