No problem at all with any warping, the Baltic Birch plywood is extremely stable, after cutting and some fine sanding the polyurethane gives it a furniture grade finish. If the price has risen like that common plywood be prepared for sticker shock, this was done some years back before most building materials went nuts.
I will make one very strong recommendation, based on a lesson learned with this project. Before cutting and doing your sub-assembly for final installation not only do you need your dimensions to be accurate but also check your dimensions from opposite corners. This is a step I didn't think about but learned when I started installation. The "cookie-cutter construction" of homes tends to leave rooms that don't have square corners. Was a real pain going up-n-down that step ladder to make minor adjustments so everything fit properly.