If you take a sine wave and run it through a circuit that does:
Y = X ^(17/19)
the sine wave's RMS amplitude will be compressed towards about 0.98V RMS and there will be some distortion. The 3rd harmonic will be about 2.7%.
Assume that the sine wave we start with is 300Hz.
A phase shifter (all pass filter) can be made with a Q such that the
900Hz, 3rd harmonic is shifted by 180 degree relative to the 300Hz sinewave.
If we take this shifted signal and do another X^(17/19) operation on it, the 3rd harmonic will only be about 0.2%
You don't need the phase shift to be exactly 180 degrees. Any non-zero phase shift and two steps of (17/19) soft clipping will result in less harmonic content than one step of (17/19)^2 clipping would produce.
If more distortion can be lived with, a lower power such as (11/13) could be used.
Since the band of interest is 300Hz to 3KHz, we don't have to worry about the harmonics of the frequencies above 1KHz. Those can be removed with a simple low pass filter. I haven't verified it yet but it seems to me that
3 stages of phase shifter and 4 clippers should be able to make a significant compression of amplitude but make less that 5% distortion on a sine wave.
The intermodulation distortion will not be made zero by this method. If the input has more than one frequency component, the distortion will be much higher.