The Illustration greys are probably close to what you want. The illustration black out of the bottle is a warm black. If you want to make it more neutral or cool it down, add some moss green, or a touch of cobalt blue. I myself keep a bottle of black with just a touch of magenta in it for helping tint portraits while keeping a warm hue to the shadows I lay down. So maybe consider just tinting your existing black with other paints you have on hand.
I do find that the white pigment used in the CI greys can be a bit picky about going through a micron at the low pressures where I like to work, so I tend to just use black, mixed with a tiny bit of another color, some transparent medium and 4013 reducer. I can dial in any grey I want by the amount of paint I lay down.
I use the CI greys when I am working with a bigger tip brush, like my eclipse, or working at a higher pressure further from the canvas, and I need an opaque cover.