So here's some early results. This is using pieces of PET cut out of discarded food containers. For both tests, half the piece of PET was treated and half not.The success of the experiment is easy to check quickly by sprinkling water on the sheet. As you say, it runs off on raw polyester, but if the treatment is successful, then it will spread nicely...
1) Sheet wiped with NaOH solution. No noticeable difference in water runoff test. A slightly sticky feel when running your finger across the treated area but the effect doesn't last. Does not look like a viable route.
2) Overnight soak in NaOH. Water spreads over the treated area and does not run off. Still runs off as expected in untreated area. Treated part of the PET has a cloudy appearance. You can still easily see through it, but it's not as clear as the untreated part.
Next step I think will be to make a test strip with progressively longer "soaks" in the NaOH and water test. See if I can identify a lower limit on the soak time required.