It could be the transmission or TC I suppose , but how one of those could cause idle rpm too-high & wandering in P remains a mystery, at least to diy’er me . Best of luck.
My guess is some sort of air leak allowing unmetered air into the engine. Ask your shop to double check the entire pathway from the sair filter to the throttle body . Not uncommon for pleated rubber boots to develop a crack in a 13 year old car. PCV and EGR problems are potential culprits too. What is the intake manifold vacuum reading at warn idle?