That is exactly what happened to me with my first child. I also had a really deep belly button and just the day before I went into labor it popped out! I'll have to look for the pict! It was so funny! We too said -oops, Turkey's done.
Maybe a little TMI but my belly button was so deep it was impossible to clean. I was amazed and disgusted by what came out of there as it reversed itself! Blech!
Jackie