I know 1/4" plywood isn't the most useful material, but it is great for what it is great for. I found an ad on craigslist for this 1/4" plywood, it's the remnants of larger sheets, but very nice stuff. There are many more sheets of oak, excellent on both faces, about 13" wide, and 7 and 8 foot lengths. $3 apiece.
I bought several 28 x 34" birch, same price, and several 20" x 8' [with a luan backside] as well as a handful of the red oak - all $3 each.
The fellow is located in the foothills of the Adirondacks, it was about a 2 hour round trip for me, starting in Utica NY, but well worth it. Here's the ad, if you respond, tell him I sent you. Real nice fellow.