I have seen Mahogany with a similar figure to that plastic wrap in the past (not a veneer though, I really didn't use veneer other than black walnut in between neck laminations).
I want to say "lace mahogany" but that might not be the right term since I have a few boards of English Lacewood has a look quite different than that.
BUT, the point is, once you have a good high-gloss finish on it, it would dance in the light like fiddleback maple does, with that long, stringy looking figure. Absolutely beautiful if finished correctly to capitalize on that.
Zebrawood might be an option, particularly with the right tint to make the whiter stripes a bit more brown... Either way, it will never be an exact match. And Zebrawood does not have that 3-D, dance in the light look either. Your best bet is to find another drum and scavenge the wrap from that I think.