Wonder if anyone has studied images of the universe for duplicate galaxies on opposite sides of us, to determine if we're seeing wrap-around.
Of course! The Hubble telescope does that sort of thing all day every day. You should check out some of the Hubble Deep Field images.
And they didn't see that. However, we can't see all that far - we can only see about 14 billion light years (the age of the universe is 14 billion years, so at the speed of light which is one light year per year any light originating further than 14 billion light years from us hasn't had time to reach us yet). That's what's called the "observable universe" - the small portion of it we can see.