Fiddling around with frequency sweeps, I noticed a large suckout around 5–6 kHz on the E3. I experimented with positioning and, as
@Dan Clark mentioned, placing the E3 forward on the head gave the best result (horizontally forward, while vertically I kept them centered on my ears). The massive dip shifted to around 7–7.5 kHz, but with much lower Q and amplitude. It seems that whatever part of the AMTS waveguide is responsible for 5–6 kHz was being blocked by part of my ear, causing complete cancellation. It might be worthwhile for other owners to run some sweeps to see if something similar happens on their heads.
Pushing them forward also added some extra low-end impact. My guess is that the pads, when resting on the bone right behind the ear and on the jaw, created a better seal. Dynamics - if that’s the right word - also improved, particularly the punch of bass drums and toms. Sweeping in that position, I didn’t notice any more major dips.
The only downside is comfort. In this position, both cups need to be perfectly aligned, and it’s less natural to wear. Still, for the improvement in frequency response, I think it’s a worthwhile tradeoff.