You are dyeing the plastic,good idea.I am going to tell you a secret. The very best black trim restorer is sold in 2 parts. The first part can be found at Walmart. No, it is not in the auto aisle.
They keep it well hidden. Head on over to the shoe department. It is labeled "Kiwi Black Leather Dye".
Now....to be clear, this stuff is so good that it will make anything that it touches black. So I would suggest taping around the trim before you apply. Put that on there and let it sit and cure in the sun for a few days. When you are certain that it is good and cured, you are going to need step 2.
Step 2 will be from Amazon. Get a bottle of Ceramic coating for cars. Do not buy the expensive bottles. You should not spend more than 20-25 dollars. Just make sure that it has over 1000 reviews and has a really good rating. 9H is good. 10H is better and 12H is even better than that.
Once you put that over the trim that has been treated with the Kiwi, the trim will look better than the day it came out of the factory. And it will last a long time in this condition.
When it eventually does fade again....depending on how far you let it go, you can just retreat with the Ceramic or do both steps again.
Speaking of blacks shoes I had a pair that didn't look good so I took a black magic marker and covered the shoes with it.
Then polished them with Kiwi(the best) black polish and they looked almost brand new.