I'm wondering if any SDR software is able to automatically fine tune a SSB signal to perfect clarifying, though no carrier or pilot tone is transmitted,
with this trick :
finding the strongest tones in the passband,
then looking to find the harmonically related ones,
then computing the exact missing carrier frequency,
and using it for the best SSB decode.
Of course, the tone content of an audio signal is heavily variable, but within a few milliseconds, sustained notes in music should be enough for all that computing work, and once in sync, the demodulation should stay in sync just like a good AM sync demodulator when the carrier goes down by selective fading.