Thanks joejet, based on this thread, I bought the Scratch X 20 at Shucks auto...$10.00 for a small tube.

It works! A few observations:

A LOT of rubbing and presssure is necessary to cut through the oxidization.
There was a dark grey residue on the polishing cloth as the oxidization came off. This product is designed for paint, and it does cut through without obvious damage. I was able to get about 1/4 of the complete surround done before my muscles gave out.

I agree, it will take about 3 treatments to remove all the discoloration, but about 80% goes away on the first treatment. This is going to take time.

I would be hesitant to use a power tool to apply this product as it could cut too deep and damage the surround or the rubber immediately surrounding the plastic.

The results require a lot of work, but are worth it.

A few hints.. wear gloves, as the polish is caustic, and keep your hands away from your nose and eyes for the same reason.

It works 10x better than the plastic polish I had used before. I think this product is the answer. With maintenance, this area should look as great as the rest of the car.

Again, thanks joejet and all: