Haven’t worked with it (yet, its on order as we speak) but my go to for cleaning anything sticky is mineral spirits, citrus cleaners or some kind of cooking oil - depending on what the surface can tolerate.
Pre-treating with one of the above and then laundry machine is what I would try.
Kind of a tangent but because I was curious I looked up “what is goo gone” and found this:
Goo Gone is a commercial degreaser we like because it makes removing sticker or tape residue a breeze. But if you’re looking to save money or you enjoy making your own cleaning agents you can make it yourself with gasoline and citrus oil.
Sounds like a bad idea to me, but what do I know - there’s a thread on here about acidifying blueberries with battery acid.