I would dig them up, put them on a tarp, water them well and cover the root ball with another tarp and they probably will not know they were moved.

This is frequently done. It is best done when the plant is dormant. It would be least successful when the plant is actively growing and the weather is hot. Rhododendrons have shallow roots, so dig a large root ball but not terribly deep. At the rhododendron species foundation they had to replant most of their plants when the saw dust they were using rotted causing a real mess. They moved the large plants by sandwiching the shallow root mass between two shipping pallets. The root ball was only about 8" thick and about 4 or 5 foot in diameter for most plants. Keep the roots well drained but moist. Use a lot of mulch to protect the roots when the plant is out of the ground.