It's perfectly normal for a canned output profile like your Epson profile to have some irregularities in an RGB neutral gradient. You typically won't ever see that in a normal color print, even one with significant neutral areas.
If you need perfect (well, close to perfect) neutral rendering, you'll need to make a custom profile of your printer with your paper, or print with Advanced Black and White printing mode, which primarily uses the gray inks with a smattering of the other colors mixed in. ABW will give you a very neutral black and white print on most papers, but if you need to print images that have black and white mixed with color, you have to print as RGB.
I've been making custom profiles from something over fifteen years now and have made countless black and white prints using both methods. Using custom profiles there is almost no difference between an RGB black and white and an ABW black and white aside from the slightly increased d-max on ABW.
If you're going to print ABW, it's best to make a neutral copy of your file, then convert it to sRGB before sending it to the printer. At least if you're using the latest OS's and drivers.
Finally, while you can't edit an ICC profile from within Photoshop, you certainly CAN edit many aspects of almost any ICC profile. The best tool to use (and of course you need a license for it) is the Edit Module in Gretag's ProfileMaker Professional. By far the best ICC edit tool I've ever used, but if you have a good custom profile, you won't have to resort to after the fact editing.