If we accept that goodness is not a natural property and only a property we ascribe by convention (which, yeah, is basically what I think) then the whole Euthyphro thing becomes irrelevant anyway, surely? Things can't be described as "Good" full stop, regardless of how God figures into it.
Well no, many people believe states and actions can be described as good without the property of goodness inhering in things.
Presumably we both think feeding a starving child is good. But why is it good? If we're nominalists it can't be because feeding a starving child is related to the property of good, because we don't think such universals exist. So the classical theist position that neither horns of the Euthyphro dilemma apply because God is simply identical with the property of good isn't valid to us. But it may be that feeding the starving child is good because it aligns with the moral law, and/or because God the arbiter of morality commands us to feed starving children.
Perhaps Euthyphro kind of crystallizes the theist position as inherently Platonic - i.e. believing in independent existence of "Good" like you said - but I don't think many theists would necessarily shy away from that position.
Sure. There are many, many theists who hold to realism about universals. It's historically the most popular theist position. But I think we have reason to reject realism about universals (Ockham's famous razor) and most philosophers nowadays lean towards nominalism, including some theologians like William Lane Craig IIRC. At the very least, it's not as simple as eviscerating the Euthyphro dilemma by saying you're a Platonist of some sort and leaving it at that: such a position involves you in a very thorny and unresolved millennia-long philosophical debate with implications well beyond the particular issue at hand.
Funnily enough, I think the entire point of the dilemma as Plato presents it in Euthyphro is that it's
supposed to lead the reader to an intimation of his theory of Forms. The start of the enquiry about the nature of "The Pious" (and in other dialogues "what is Justice" etc.) is almost a form of question-begging by Plato that assumes universals are real in the first place.