Any area that is a different shape to the Refit is also sliced off and dragged away, until we are left with pretty much only the central core of the saucer and some surrounding decks remaining. Essentially the keel or 'backbone' of the original TOS saucer is still there, so it's arguably still the same ship.
If/when you get around to doing this, remember that the refit saucer has a greater diameter than the TOS saucer, so it will need to be cut off and reattached to match the larger diameter.