The adhesive backed veneer does a nice job. Time will tell how well the adhesive holds up to the various "weather" conditions in a car. I know that its better than it was twenty years ago. That said, as you saw Bavbob's nice job on pg 1 of this thread, remove the wood first to get a professional look like his. You can't get a decent fit and finish while its in the car. I know some folks in the past have said it can be done, but you'll have a nasty mess, and probably regret it... Drew's comment is spot on, that its what you see while driving, so you'll thank yourself every time you fire that mother up, for doing it right.
Touching up caskets, huh...that's a pretty thankless job. Make it perfect and then plant it six feet under.