Well, I tried the Oxyclean and it did the trick, for the grab handles at least. It didn't quit clean the ceiling material itself, as I had expected. Maybe I need to use a stronger solution.

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1999 MB SL500 (110,000 mi)
2004 Volvo V70 2.5T (220,000 mi)
2014 Tesla Model S 85 (136,000 mi)
MBCA member