I would talk to a custom interior shop to see if it can be sprayed or wiped with die.

There are sprays and wipe on dies for carpets. I have used the wipe on to make black carpet look like new and even smell new. I would think the shorter nap on the headliner would make it easier to die though gravity would working against you.

It would be nice to test it on something but that's the reason to pick the main brains at a custom shop, to see if it can be done and if it takes a professional to do it right.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas