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I used "WypAll Green Cleaning Wipes" and "Dr. Schumacher Orange Solvent."
The cleaning wipes alone would certainly have been sufficient, though.
They must contain a solvent that works effectively against the soft-touch coating.
By repeatedly wiping over the surface and using a plastic wedge I was able to lift off the sticky layer.
As you can see in the photo of the power window switch panel, the soft-touch layer can be neatly pushed together and lifted off using the wedge.
Looks good! For future reference, that small trim piece is held in by four clips. Disconnect by prying the bottom edge away horizontally from the pillar/grab handle toward the shifter. Work your way up to release all four. Snap back in evenly to reassemble.