If I'm reading this right, the screws are out, but the wood cover is stuck, correct?
Best option for the wood might be a bit of hot glue. Blob some glue on one of those plaster spreading things, gently press it against the wood, let set, then gently lever the wood piece out. You should be able to peel the hot glue off the wood with a bit of care after that.
Or gently hook a couple of screwdrivers into both of the holes and see if you can get it moving that way.