Hi Oliger,
Neat project, I had a couple things to mention, no promises any of it will be helpful though..haha.
First, those vinyl tiles are what were in my parents kitchen for years. They installed them in mid to late 1999, and I believe they were from Armstrong. Bought them at Lowe's or Menard's at that time which is when they built the house they currently live in. I always liked those tiles, the pattern always seemed old fashioned/vintage looking to me even in 99' when we layed them, It's kind of neat to know now, from your history, that the pattern goes at least back to the 1980's if not farther.
They replaced the kitchen floor about 3 years ago due broken tiles from chair scrapes and a couple of 'floaters' that lost their sticky from a water leak near the sink, but the same yellowing happened to their floor as well. It was mostly concentrated near their double patio door, where the sun hit it. They still have this floor in their laundry room, where they decided to leave it as is since it didn't have as much wear and tear there. Funny to see it in a picture online like this, but then we're both Hoosiers, it's a popular pattern out our way I guess, haha.
The second thing I want to mention is Sarah's suggestion. What she's referring to is called Retrobrite. It's not an exact product but rather a "recipe" someone concocted to reverse the yellowing/browning effect that occurs in different types of plastic as it ages. It was first used in restoring old Computer Hardware.. Monitor and PC cases, Keyboards, etc. that once were white but had developed a patina over the decades.The Retrobrite recipe uses high concentrates of peroxide and some other things to chemically reverse the yellowing process in some types of plastic. you can read about it here
en.wikipedia.org
There are some drawbacks in your situation for it not being a possible solution. The first would be that it is supposed to only work on ABS type plastics and Vinyl flooring may or may not be effected in the same way.
And the second issue is that the Retrobrite process requires direct sunlight to do it's thing. Parts that are meant to be de-yellowed are covered in the mixture then placed in a plastic bag, the bag is then left to sit outside on a warm day in full sunshine for several hours, rotated occasionally to get exposure to all sides. It's a combination of the UV light and the heat that reacts with the chemicals that causes the whitening reaction.
It's a good idea definitely, but might not work for this application. I used it once to de-yellow a vintage cap to an old Downy bottle from the 70's and it worked a treat.
