Just briefly, my first subtracition spectra:

Much better than I expected, but also not good enough. All spectra in this plot (except for the constant noise model) are averages over 10 simulation runs. The NN is the average NN, and the two "res." curves show the residual after subtraction. It seems that the frequency-dependent linear estimator is working since subtraction performance is consistent with the (frequency-dependent) SNR. Remember that the total integrated SNR=NN/noise is much smaller than 1 due to the low-frequency noise, and therefore you don't achieve any subtraction using the simple time-domain linear estimators. Now the final step is to improve the subtraction performance a little more. I don't have clever ideas how to do this, but there will be a way.