This is a difficult one I don't think we've come across before unless someone else remembers it. The best I can suggest is the electrics are working on the selection side as the led's/dash display correctly. It's generated from the physical position of the lever. It's sounds as if it's reporting correctly. A code read would confirm as I would expect an implacable selection type fault code if it didn't.
That said the only thing would be an oil change which can work wonders on these auto's. It can solve all sorts of strange problems. Also check the barrel connectors are tight together and clean inside.