I have the same perception of colors, 4C looks yellowish and 3C/3D looks very close to ideal white. Did you received E2L 5700k? How does it look in comparison with 3C/3D tint?
For Cree XM-L2, emitters with tints 3A-3B-3C-3D exist mostly up to 70 CRI (maybe some of them are 75), the 4C /which is common in many Convoy lights/ is 75 CRI.
Initially I was sceptic with a CW emitter in general, but later I bought an E2L 5700K, and that was one of my best purchases.
With the color rendering ability of Nichia 219C (which is available also in 90 CRI - and Jaxman lights use that), a cool white is not anymore ‘crude’ in any way.
The best description for that tint is ‘rich pure white with a slight hint of coolness’.
Do believe, that once you get an E2L 5700K (Nichia 219C), all of the NW or CW Cree XM-L2 tints will look ‘crude’ 
Received today 5700k. It’s really pure white, not yellowish/greenish like 3C or bluish like 1A.
I use the 4000k Nichia as my torch in work and love it.
Tried to solder stars on the driver. Here are results:
star 1: 2.12A > 1.04A
star 2: 2.12A > 1.04A > 0.25A > 0.02A
star 3: 2.12A > 1.04A > 0.09A > SOS
Light.
This old fart has Nichia219B or Cree 5000. in 90% of his torches.
Shade of light is MORE important then throw distance any day
Specially when you eyes get up to the late ’70s.
Watery too.
Regarding below………
“”“Wellp, let me use an audio analogy…
When listening with my Bose earmuffs, the sound’s got nice crisp highs that really come out clearly.
I’ve also got a pair of Sennheisers, somewhat infamous for “the Sennheiser veil”, ie, treble response is somewhat muted, as if the sound’s coming from “behind a veil”.
As comfortable as the Bose earmuffs are, the sound gets a little fatiguing after a while.“”“.
BOSE were originally developed as an “ALL round sound”.
NOT Stereophonic. and advertised as such.
I was around then and an Audiophile.
Senn’s were always touted as studio . BUT. You want the true sound of music.
Try a set of STAX Electrostats. Or Koss. (in the old school)
My Senn’s veil the trebles. BUT. At my age.
My heariung or lack of. dimms everything
I used them as my Headphones. then Yamaha when on yacht and CD’s came out.
They were a nice copy of the Stax at a paupers price (mine)
with KEF Dual B139 Labrynths. for speakers (7ft tall. lead sheet lined, on concrete floor bases)
when orchestral and Organ Direct cut discs were on.
This in ’60s through ’80’s. (breeding kids) Then lived on my yachts till last 18 yrs.
Cold white light looks totally “flat” and dead. You need from 5500 down to give any colour when not searching distance.