Synthetic as it is, I had some success in the past, giving a similar fabric a date with some black dye, so I thought I'd try it again. Tossed the curtain in with the black dye, hung it out to dry and this is the result :
My camera does not give it quite the right color, but it is now a more olive tinge and noticeably darker, which is what I wanted. Now I can continue with the next stage of the jacket I want to make.