If it's solid wood, there is a high chance that it will warp with changes in temperature and/or humidity. I guess it is some kind of plywood made from birch wood. Plywood is much less prone to warping due to the aforementionned external factors. In the end things might be different since the plates will be under pressure. I'm wondering if a structure a bit similar to what you did for the PLA endplates in the small battery might work. That's off course only if you run into trouble with your current, simple design.