All wood and dimensional lumber will move with temp and humidity. Engineered lumber such as plywood has a flatness tolerance that is pretty generous. So .009 is nothing I would worry about. Shim it out today check it when the season changes it may surprise you how much it can move. Especially if two different materials are fixed together with glue. I screw the homosote to the solid core door and the screws allow the homosote to move eliminating warping.

There is more than a good chance simply shrinking the covering will result in more than .009 change.

Dennis