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You could go to a lumber yard at and see if they have 10" to 12" boards. They should have them in different lengths and some stores can cut it for you. If not, some stores sell plywood with different veneers on them, but you might have to buy an entire sheet.
But since it sounds like this will be under the computer anyway, does it really matter whether you have the veneer or not? If you get plywood with veneer, the edges will still show plywood.
Perhaps consider something that has similar color like maple or oak? If you need them darker, you can always apply a stain.
I was at a lumber yard awhile back and they did have 1x8 boards in lengths from 1 or 2 ft all the way up to 12 ft. I don't remember if they have 10 or 12 in boards or whether or not they had birch. I know they had maple, oak, pine, redwood, and walnut for sure.