If one prints only black and white, the solution I use is to have most of the channels/carts be 100% carbon pigment -- at different dilutions. Only one position is a color "toner" to give me control of the print tone along a straight line from carbon warm to "neutral" (which I happen to think looks better with a slightly positive Lab A). I at one time used B&W inksets with full color control, but I found most people can't control the tone unless it's pretty much in a straight line -- i.e., limited variables.
See, for example,
http://www.paulroark.com/BW-Info/7800-Glossy-Carbon-Variable-Tone-2016.pdf .
Note that I use 2 MK positions to get a good dmax on Arches watercolor paper. I don't recommend most use this. Without the need for 2 MKs, the inkset approach would be like the 3800 setup described here:
http://www.paulroark.com/BW-Info/3880-Carbon-Variable-Tone-2015.pdf , but I'd substitute PK as the starter for MK now, as the newest MK does not seem to have any advantage to PK in terms of being more neutral. On the flip side, nothing is less expensive than a matte paper only B&W inkset using my generic dilution base (c6b). See
http://www.paulroark.com/BW-Info/Ink-Mixing.pdf The blue-cyan mix in the toner is where the Lab A can be adjusted if wanted.
In my view the Epson LLK is greenish. I doubt it is 100% carbon. I'd guess it's a combination of carbon and cyan pigments. My experience is that different pigment types tend to separate somewhat. As such, it might be a good idea for people seeing a hue in their Epson "neutral" inks to agitate them (as well as all the carts) periodically. Pigments settle slowly.
BTW, if you're in the Santa Barbara, CA area from mid-Feb to mid-April, stop by the Elverhoj Museum (
http://www.elverhoj.org/index.html) to see a show of my B&W prints. (I have a map linked to my home page, URL below.)
Paul
www.PaulRoark.com http://www.paulroark.com/BW-Info/