Look at Joshua parsing the Greek! That makes me so happy!! (It's kind of fun, isn't it?)
At first read, I don't see anything wrong with your parsing of χρυσοῦν. Here's the Wiktionary entry for the Attic form of χρῡ́σεος
https://en.wiktionary.org/w/index.php?title=χρυσοῦς&oldid=55002924
But if it's from χρυσόω, the present active neuter participle would be χρυσοῦν with the same circumflex over the upsilon. So you're spot on there from my meager knowledge.
Joshua 's analogy of "flat" Plato to "gold-leaf, gilded' Plato is intriguing! Gold leaf is really flatter than flat. It's barely there.
Another possible source *could* be, since we're blue-skying it - or even a complement to Joshua's idea - is that Plato just gilded himself with his teacher Socrates' ideas or used Socrates to gild his own ideas.
Since it would be a present active neuter participle, it would probably be translated as "Gilding" I think, so "Gilding Plato"? The one who is gilding? "... And Plato himself gilding." Even so, no matter how that sentence is parsed, the χρυσοῦν < χρυσόω option raises some intriguing possibilities!
Thanks for the food for thought!! Great job!