I can make this work in an Avid. In AE pre-comp your graphics build and place it over black in another comp. Then apply a levels effect to the pre-comp, set output black to 16 and output white to 235. Render out to Animation codec. Import this into an Avid while setting the source as 601/709 (rather than RGB, which it is). The conversion on import will restore the white and black points. Since the background black wasn’t altered by the levels adjust, it gets pushed down to the bottom (-10 IRE).
Following the same logic but bringing the clip into Final Cut (regardless of the codec it was rendered to) doesn’t work as it is not possible to push black below 0 IRE. It simply clips at that point. Perhaps a third party color corrector might allow this?
As AE processes in RGB, there simply isn’t any black less than black. Blacker than black and whiter than white (which FCP does allow) are built into video standards (analog and digital) as a safety margin.