Had you been schooled in a tradition that included Latin grammar, you would have known that this is a perfectly reasonable classical construction. It is called the ablative absolute.
If you are going to be a compulsive grammarian, then you need to understand the rhetorical tradition underlying the sentence construction employed by the classically educated world, a world that has sadly shrunk to such a state that someone like you can post something like this, calling himself a compulsive grammarian, and get away with it.
None of us are perfect, but when you take out a sword and wield it, ensure it has not been dulled by time and ignorance.
I don't understand your "underlying rhetorical tradition" argument. A dangling modifier is simply an illiteracy in modern English usage.
It really doesn't matter how Ovid used to phrase it because--news flash--HE WASN"T WRITING IN ENGLISH. I write English.