Figured I would add my experience just in case it would be helpful for anyone in the future.
I bought a used Macbook Pro a couple of weeks ago with quite bad Staingate. At first, I used the Listerine and that worked a treat. Got about 90% of the screen in like 5 minutes. But then, like many others, I was left with a really robust part of the coating in the upper region of the screen. I tried Listerine, the W5 wipes, cleaners, Polywatch, and a lot of elbow grease for 1 hour - not any improvement.
I was close to giving up but then I tried a mixture of 1 part vinegar to 2 parts baking soda, and this did the trick. I'''f you're like me and have this part of the coating that doesn't want to give, I recommend this'''. Use a microfiber cloth, and I actually recommend rubbing the vinegar/soda paste into the cloth (the abrasive baking soda grains is what removes it I think), before applying it with medium pressure to the screen in small circles. That way you pretty much a slightly abrasive cloth, which removes the coating. Took me about 45-60 minutes, so have patience, but you will see it starts wearing away bit by bit.
I’ve added some photos. Left is after the Listerine, where I have the robust, impossible to remove, remaining coating. Middle and Right are one after 30 minutes of me rubbing with the baking soda, and then a perfectly clear screen after 45-60 minutes, respectively. It should be quite clear which is which.
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