"what the ER4 produces may be truer to the recording, but the sound from the GR07 is truer to what you would hear in everyday life."
Correct me if I'm wrong, but are you implying that it's the recording that is not containing "what you would hear in everyday life"? If that's the case, it's not the ER4S's fault, it's the recording; and any realism that you would sense from the GR07 would then be a distortion that brings that sense of realism to a recording didn't originally have.
"Note weight" is a tricky thing for IEMs. With loudspeakers, weight is generally not an issue even with flat response. With IEMs, a flat response may detract from some of that realism, but a boosted bass response can get in way of higher frequencies.
Again, I don't hear any less decay and reverb from my Etys than I do from my EQ'd GR07. That tells me that the reverb you're referring to may actually be more of a function of more intense bass response than actual decay.
Part of our perception of bass from loudspeakers comes from bone conduction. The low frequency notes move air that physically impacts out body, and it is entirely audible. Tap your finger against your head behind your ear, it's actually quite loud. Headphones, and IEMs in particular, do not have the same effect, so some small degree of bass boost can make them sound more natural. The ER4s are almost ruler flat, which explains why they might not sound as "natural" to some people. They do, however, accurately reproduce the volume of the frequency on the recording, just not the visceral impact of moving air.
The ER4 are designed as reference-grade headphones. They're designed to replicate the source with all of its detail. In that, they succeed. The GR07 is tuned as a stage monitor; they are boosted slightly in bass and in the "presence region" of the treble to maintain definition and body in the noisy environment of a live show. In that environment, however, they sound closer to the ER4, to neutral.