sticky plastic
Well, I have now spent the day trying to clean off the stickiness, and I can report that indeed the alcohol will remove the sticky coating. Sadly, whats underneath the sticky coating is not always pretty.
My results:
The ends of the dash (normally hidden by the door when the doors are closed). All the stickiness is gone, but in place of it is an extremely dull surface the looks white in strong light. I had to put Armor-All on it to make it stay dark. (I normally do not care for the look of Armor-all).
Front dash area, the half closest to the driver and passenger: The textured area did not need anything as it was not sticky to begin with. the Center and the surround for he instrument cluster both required a lot of work but came out a really dull flat black. This includes all the area around the radio and interior air controls - vast amount of stickiness there. Lots of rags and lots of alcohol.
Front dash area, the half closest to the windshield: haven't gotten to that yet.
black surround to the door locks - came out ok.
light covered plastic (in my case) on door handles. Removed all the texture, and the resulting color is not an exact match, but much improvement over the sticky mess. You can try to only remove the top layer, but it will just come back. You have to remove all of the soft plastic that is coated onto the harder plastic below.
Between the steering wheel and the dash: There is some softer plastic here that in my case had a white tint after the stickiness was wiped off. Again Armor-all darkens it back to a more or less black.
Lots of work still to go, it took forever just to get the above areas. The dash ends (up against the door when closed) were as sticky as any other, and since that area would normally not see much sunlight at all, the failure of the plastic must be time (mine is a 2000 new beetle) or temperature, not sunlight. I went out tonight and bought a bigger bottle of alcohol, so I am ready for tomorrow.