I've done a great deal of this type of delamination repair that has held up well. Here is my suggestion.
1. Use lexan instead of new luan . Scuff up the same thickness lexan and drill some small holes in it to grab better.
2. Use Gorilla glue. Moisten the area then slip the lexan repair piece in after both sides have been painted with glue.
3. Use an expanding cargo bar (available from northern and other tool supplliers.)
4. Brace the cargo bar against a building wall.
5. After drying cut off excess gorilla glue, caulk any gaps with proflex and replace molding.
