One permaculture principle I think best suits this problem is to produce no waste. Even though that is impossible to do overnight with the rate of plastic used and discarded everyday, it is an important concept to keep in mind to lower the plastic we do use. We are used to using disposable products, throwing away everything after we are done with it. But, we need to change our mindset in order to change the condition we are in and to fix this problem. If every human thought of this principle before purchasing a bottle of water or using a plastic bag, the number would probably decrease over time.
The place in this system to intervene and use this principle is in the materials being used. As artists and designers we must select our materials consciously with the longterm affects in mind. One solution to the problem of where the plastic waste goes is recycling it for other uses. Rather than the plastic sitting in the ocean, we can reuse it for a different function. Making this problem more sustainable means giving the waste a function. Therefore, using it as a material for something else would balance the production and the waste.