Mid-sized black plate options
You can piece together a 16x16 black plate in two layers, by making a base layer consisting of 3867 - Baseplate 16 x 16 (not available in black, but Dark Bluish Gray is a good option and given the minimal thickness it won't show)

 

and then putting 4 of 41539 - Plate 8 x 8 in Black on top side-by-side.