I found a time slot to refine my simulation. Octave script is attached. Also attached are some plots generated by the script. Compared to the initial attempt I have reduced the sampling rate by from 43.2kHz to 10.8kHz (=2700*4), in order that the FFT size at the receiver can be reduced to 128 (to lower the computational complexity). Clearly this also reduced the noise immunity, which can be seen in the eye diagram. For comparison, an eye diagram for a noise-free channel is attached as well. Hard to estimate so far, how other channel deficiencies degrade the demodulation. Phase does not matter per se, since the demodulator output is the magnitude of the complex frequency bin, but group delay differences certainly do matter. 1ms might still be tolerable, but not significantly more.