Bill, I wouldn't say that "nothing would exist" because that treats nothing as an existent. No, it doesn't. Suppose I said, "I have nothing in my safe." Would you conclude from that that I was treating nothing as an existent? If you would, I'd think you were a pretty strange dude. Clearly, if I said, "I have nothing in my safe," I would simply mean that I didn't have anything in my safe. And that's exactly how the skeptic meant it in my dialogue. Remember, he is questioning why there is something in existence rather than nothing. He is not treating nothing as if it were another kind of something.
But now that we are clear on what the skeptic is saying, do you not agree that your rejoinder is insufficient to refute him, as he would reply that if nothing (i.e., not anything) exists to begin with, then nothing would exist to cause existence either. So why does it exist? Why is there something rather than nothing? It won't do to reply, "What could have prevented it?" for he would respond that simply because there isn't anything that could have prevented it doesn't explain its existence, for if there wasn't anything to prevent it, then there wouldn't have been anything to cause it either. Again, the only effective answer is simply to point out that any attempt to explain existence presupposes the very thing that one is attempting to explain.
Saying that "no thing prevents (makes impossible) Existence" is not problematic, (so far as I can see) because it is not implying the existence of a naught. It is simply the negation of the false statement that "some thing prevents Existence." Since Existence does exist, it is obvious that Existence was not prevented by some thing. If Existence was not prevented by some thing, does it not follow that no thing prevented Existence? Yes, but however true it is, your statement doesn't satisfy its intended purpose, because it doesn't answer the skeptic; it doesn't explain why there is something rather than nothing, which is what he is asking.