Hi,
Clipping at higher volume is quite expectable.
Clipping means that the supply rails limit the output signal.
Thus - besides the chip - the power supply is reponsible for clipping.
What exact power supply do you use? Electrical specifications please.
Since it seems to be a bridged output stage, your power supply should be able to provide V_supp / 2 Ohms of current ( I = V / R).
For a small speaker it is impossible to produce deep frequency bass. Thus it makes no sense to amplify those frequencies, because the membrane will just move without useful audible sound. This unnecessary movement will cause distortion in the speaker, but it additionally limits the amplifier's range for useful, audible frequencies.
--> focus on the audible frequency range.
Thus - depending on your speaker - an lower cutoff frequency of 200Hz..500Hz should be used.
This means an input capacitor of 22nF down to 10nF.
Klaus