I've been trying for a long time to figure out how to deal with a bunch of "sticky" interior plastic. It's this way all over. The airplane came this way from its first owner and fixing it has been been bothering me for a long time, and I'm finally going to ask for help! The best way to describe is as if there was an adhesive poured all over it. Goo-Gone with a polishing pad used by hand has certainly helped, but it's all still very sticky and noticeable. I've also tried Nextzett (1Z) Cockpit Premium (aptly named!), which also helps a little. Being so sticky, it collects every drop of dust, hair, and other contaminants and quickly looks very dirty. Like my car, the airplane sometimes bakes in the hot sun. I have no idea if its an artifact from that, or the original owner did something bizarre. Regardless, it's been a challenge and so far I have not been able to definitively clean it up. At least I haven't made things worse. As far as I know, there is nothing special about this trim. It's just plastic trim. Picture below:
So this is way late in the game but figured I'd answer in case you were still interested in a solution (or someone else was)... Looks like a lot of the wrong kinds of cleaners were used on this dash (something like a degreaser, Simple Green, etc). At this point, I'm not sure that it's a matter of cleaning but more a matter of repairing. Cockpit Premium wouldn't do much. If it was a matter of cleaning/removing a type of adhesive residue, then nextzett Plastic Deep Cleaner would be the solution because it's a straight up detergent cleaner that's ready to use but isn't too aggressive (just make sure you apply as directed). I think at this point you wouldn't have much to lose. If anything, I'm sure PDC would be very useful in cleaning up the rest of the cockpit! Hope that helps!