Filtering signal with added noise (frequencies known)
You want a Wiener filter here.  Basically your frequency response at frequency $f$ should be $\frac{E |S|^2}{E |S|^2 + E |N|^2}$ where $S$ is the Fourier transform of the signal and $N$ of the noise (all dependent on $f$ of course).  So your filters should not aim for a stop band of zero but rather a stop band that will admit an amount of signal based on the expected SNR at that frequency.

There are comparatively few staircases in the total resulting frequency response here, so you might consider going for forward and backward in time IIR filtering (netting a zero phase delay, with normal delay the Wiener filter design becomes pointless for more than a 90degree phase shift) or some FFT with windowed overlap-add filtering.

Wiener filters like that minimize the expected mean square error, so they seem to be the right tool here.