Is it possible to move the coordinate of a MKAnnotation without adding and removing the annotation from the map?
Don't know whether it's more generally possible, but it is if you have your own custom MKAnnotationView.
I was able to adapt the approach documented at http://spitzkoff.com/craig/?p=108 by Craig Spitzkoff:
You could likely simplify this approach further - you may not require an internal view object in all circumstances.