You shouldn't expect a black dye mixture to produce a perfectly neutral grey unless the dye seller specifically promotes it as being good for that. Normally, if you want a grey that is made from a dye mixture (and there is no unmixed single-dye black or grey in the Procion MX dye line), it is best to buy a dye mixture that specifically has "grey" (or "gray") in its name. It saves a lot of trouble. Dharma says that their Black is dark green, their Better Black is purple-blue, New Black is blue, and Jet Black can be greenish. (I've had kind of brownish results with Jet Black, myself.)
Jo's advice to screen out the larger particles of red from your black mixtures might work out perfectly. There's also the option of using a diluted navy, such as blue MX-2G (cobalt blue or mixing blue).
If you have a purplish grey, you can indeed turn it to a neutral grey by adding just the right amount of the color that is opposite it on the color wheel. You get a brown only if you use the wrong amount, or choose a color that is not quite opposite on the color wheel. However, since light purple is okay for your purposes, and light brown is not at all okay, it's probably better to skip trying to reach a perfectly neutral grey.
The easiest way, in my opinion, to get an accurate idea of exactly what color is opposite on the color wheel is by staring at the colored item without a break for a solid minute, then quickly turning your eyes upon a neutal white surface. Your eyes become fatigued of whatever color you stare at fixedly, and thus the white for a moment or so looks like a color. For example, if you stare at a bright scarlet piece of dyed fabric for a minute or two without shifting your eyes, then look at something white, for a moment you see turquoise.
It can be difficult in direct dye application to keep a dye mixture from separating out into different colors; you almost always get a bit of a halo of a different color. My favorite black fiber reactive dye is not a Procion MX dye at all, but is instead a
Remazol type dye. You can buy it locally if your fabric store carries "Dylon Permanent Dye 12 Black". (
NOT Dylon Cold Dye or Dylon Multi-Purpose or anything like that - it has to be Dylon
Permanent to contain this particular unmixed black dye.) The neat thing about this dye is that it does not separate out at all, because it is a single-hue, unmixed pure dye. Look at
this link to see a comparison of Black MX-CWNA with Dylon Permanent 12 Black.
Paula