Based on further tests using my monitor's ePaper mode, which turns the screen monochrome, I would recommend #BDBDBD for the shade of grey. I got this value by taking the highest value in the blue color of #5984BD and applying it to every component of the color. The current value of #909090 has each component only slightly higher than the middle value of that color, which may account for why they look more alike on a monochrome display.
Based on further tests using my monitor's ePaper mode, which turns the screen monochrome, I would recommend #BDBDBD for the shade of grey. I got this value by taking the highest value in the blue color of #5984BD and applying it to every component of the color. The current value of #909090 has each component only slightly higher than the middle value of that color, which may account for why they look more alike on a monochrome display.