Bass traps are most likely to reduce the height of the peaks, but do little to the valleys. The valleys are result of speaker-boundary interference, the reflected waveform from a wall – usually the front wall – mixing in with the speaker’s direct radiation, and canceling it. If you had very thick and large panels behind the speakers, that would reduce the level of this reflection. Dip of 20 dB suggests that the wall is bare and reflection unattenuated, and the frequency 100 Hz suggests that distance between speaker’s front baffle and the wall is about 86 cm. Halving that distance would move the cancellation up to 200 Hz which is far less objectionable.
A small battery in form of large capacitors must be carried inside even the most modern class D amplifier for the simple reason that periodically, the voltage between the AC rails is zero, and such amplifier can’t get any power from the outlet. So it has to have tiny charge inside to still keep producing output during this dip. It’s just fact of life with AC.
The way this could be measured is via the voltage ripple, which is essentially the sag in output of the power supply when your energy draw during the dip exceeds the equipment’s store of electrical energy. So you can directly observe if your speaker load exceeds amplifier’s capabilities, by comparing the stability of the power supply’s output, I guess.
I’ve no idea why they think that having negative feedback is any issue, here. Seems completely unrelated to me. If anything, I’d say negative feedback is what makes your amplifier amplify correctly, at least to the limit that its other parameters allow.