I would print three colors, White, Black, Grey
I would combine the Ampersands and set 2017 onto one screen and print solid grey, then overprint some of the distress from the ampersands with the black.
I'd make the people and Baileys text all white so it pops better.
Depending on how much you like the customer, maybe split the black halftone from the solid black so you have four screens but three colors. That way you could use a different black, or do the texture in water base and the foreground in plastisol so it has some shine and sets it off from the ugly distress in the background.