Why are strong accents causing a problem?
Below, on the pink-blue pic, there's a frequency response of two different double basses recorded by microphone (FFT, playing a whole blues 12bar in E). You can see that the first peak is about 60 Hz. Below, the subsonic rumble is more or less unimportant for your ear. For better understanding, see the 'phon' curve - this shows how our ear percieves 'the same volume'. To the ear, the 30Hz is about as loud as 4 kHz.
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The yellow-green pic below is how the same basses, playing the same notes, behave frequency-wise when lined out through my amp. This is not the raw signal, it's processed by preamp, which (among other things) is limiting the lows by not very severe high pass filter.
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These lines show 'distribution of power' aiming from the amp to the speaker. The biggest difference is on the left side: you can see that about 50% of 'power' is taken by the frequencies below 100 Hz. If you compare the two pictures, you can see that the amp creates much more power below 60 Hz than the acoustic bass does.
The last picture is the same two basses, through the same amp, but microphoned from the speaker.
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You can see that below 60 Hz, the signal drops rapidly, because my 6" speakers are not able to reproduce such a low sounds. But, if you compare with the first 'acoustic' pic, you can see that the overall shape of frequency response is very similar.
Conclusion:
a/ big amount of 'power' is 'wasted' on subsonic rumble, which will not be reproduced anyway.
b/ if you play more loudly, the loudnes would show in the right side of the pictures. Louder playing has impact on higher harmonics of the string, but these higher harmonics need much less power to be reproduced.
So:
If the AER sounds nice, it would probably sound as nice with a HPF, but would 'spare more power' for the frequencies that are important for the overall amplified sound. Try it.