I have been pondering on your problem, and I don't think its anything to do with the filter. Consider a 300KHZ squre wave, this has got harmonics at X3, X5, X7 etc, now if you PWM it with a 10 KHZ sine wave, You get a sideband at 10 KHZ, 300 +-10 KHZ, 900 +-10 KHZ. Your LPF has to reject any thing higher then say 100 KHZ, only allowing the base band component through. So how can it generate 20 KHZ, 30 KHZ etc, i.e. base band components of distortion?
One normal attribute of a class D amp is to recover the energy in the frequencies rejected by the LPF (hence the inductive input impedance) and return it to the Vcc supply. The Vout(FOUT+&-) of the amplifier IC shows severe clipping and it should be a 300 KHZ PWM signal, so what is going on here? Has your CRO got a restricted bandwidth? There is also a little zener diode circuit, has this been used correctly?
Frank