Epson is providing an 'Advanced B/W Mode' - ABW in drivers of newer A3 and A2... printers which let you adjust the color tone of the gray level from sepia to steel blue - with neutral somewhere in the middle, and this separately for the lighter and the darker grays. But you need to do a few test prints to find that gray tone you are looking for.
But be aware - you cannot change the colors of the endpoints of the gray axis - these are the whitepoint of the paper and the blackpoint of the ink on a particular paper, there are no other colors with the same L lightness which can be used to substitute these colors.
I don't know if the L1800 provides this ABW driver feature, the ET-8550 has it, the P900 has it and other printers as well.
Can a profile correct grays to neutral - yes and no - only to a degree - it's a question how the profile software handles that - how the gray axis is connecting the whitepoint and the blackpoint, this can vary with the rendering intent. And some profiling software let you influence this . This all would require testing if particular software settings meet your requirements. And be aware that the color temperature of the ambient light influences the look of gray tones as well - particularly the lighter ones. A paper does not have a neutral spectral distribution of the paper white aside from the effects of UV additives giving just the lighter grays a more blueish tint under daylight.
So it's all a little bit more complex.