The key is for the BG to be -2.5EV compared to the subject for BG to be 'black' (this is true no matter what color or lack of color in the BG...the fundamental brightness) Since the inherent color is black already, you have a start at the -2.5EV, but your subject light falls on the BG so that it is maybe -2EV and getting captured as that 'charcoal'
Velvet could help but there is a bit of inherent sheen in velvet material fibers, making it hard for the BG to disappear wihout careful control of any ripples in the surface which will reflect back some of that sheen!
Michael88 is on the right track with his suggestion. The subject is 6' in front of the BG, so if the light were 6' from the subject but positioned at the side, the light falling on the BG would have brightness of 0EV compared to the brightness at the subject. The key is to get the brightness falling on the BG to be -1EV or more to keep that black material blacker. Move subject farther from BG, or flag off the key light so that it does not fall on the BG