HD sells luan that's a honduran mohogany veneer over a particle board core. It's cheaper than spanish cedar and has very a similar hydroscopic response. As best as I can tell the glue used doesn't impact the cigars. You'll also probably want to focus on the seal. Foam insulation tape, also available at HD, works well as does silicone aquarium sealant, also available at HD. Definitely post pics and progress updates as you go. It sounds like a cool project.
Todd
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