I doubt I'd agree to print the image as-is. I'd pull it into Photoshop & see how it could be tweaked. My first stop is Image>Adjustments>Shadows/Highlights to see how much range/underlying data I've really got to work with. I'd aim to get rid of the "mud" in the dark range, and see how crisp we could get it. For limited color b&w, my approach is always to bring out as much clarity & definition as possible, at the expense of more natural gradients. It ends up a little more stylized, but I think it prints & "reads" better that way.
Disclaimer: I am not widely experienced with high-end photo-realistic printing, and my approach has been tailored to customers who rarely pay for more than 2 inks for such things! I'd fully expect my typical customers to want this done in all black, and to consent to black + 1 grey after I pushed them. I try to give them as clear of an idea as possible of what outcome they'll get based on what they're willing to pay for.