Bellissimo, Poakwoods!
I wanted to do this with the 1/72 Bandai's, but I got stymied on the lighting of the ships.
My plan, and which I did make some tests of, was to use black velvet, photo mounted on foam board, similar to what filmzy suggested.
Fiber optic, of various sizes, looks amazing against the black void of the velvet- though you you can still pick up some shadows from objects in front, depending on the room or dio lighting.
Otherwise, I absolutely love the frame around the backdrop as well as the sensational job you did scratchbuilding the DS tiles.
Who cares about screen accuracy? You recreated the visceral impact of the screen moment in a very aesthetically pleasing way.
Bravo!