Black starboard

If you want to ship from Michigan try Wolfs Marine at 269-926-1068. They have a lot of starboad in stock.

They are preparing for a two day open house for this weekend. You might find them a tad busy right now.
 
Buy 1/2 inch and take of the difference with a router or laminate trimmer. presuming you don' need theh second face with the original texture.
 
3/8" thick, I don't know. When I fabricated my flush mount panel out of black starboard, I used 1/2". I bought it at Boaters World.
 
2 hrs south of you there is place in Dorchester Ma. called J. C Freeman . They are kind of tricky to get to, but they probally have it . They specialize in plastics.