Viburnum Tinus - transplanting

Hello! I live in Tacoma WA. We have two Viburnum Tinus plants that we would like to transplant to other places in the yard. They have been in the ground about three years and are large -- about 10 feet tall and rather sprawling. Very healthy. The base of each plant is situated about 3 feet away on all sides from Emerald Green arborvitaes and rhodies.

I would like to know approximately how deep and wide the root system for the Viburnums might be. Is this a hopeless plan? Is it possible to transplant these without damaging the plants or others nearby? Should we wait until winter to do this? (It is March 23 today).

Roots can be quite extensive when the plant is as large as you describe.
Here is how I would approach this problem:
This is sort of like digging them up slowly, so you do less damage to the roots at any one time, and the plant starts forming new roots while it still has a lot of old roots to keep it going. Remember when you start laying out the project that soil is VERY HEAVY, and it will take many people to lift the plants out of the ground. For example, if you dig up a root mass that is only a 12" cube, the soil will weigh about 100 lbs, unless it is really high in compost. The plants themselves are also quite heavy. A 12" x 12" x 12" cube is nowhere near large enough to retain enough roots, though. I would start with nothing smaller than 24" x 24" x 18" deep. (600 lbs if it is sand-silt-clay type of soil). Think of a nursery container that is referred to as a 24" box. Go see some, and see how large a plant is in one. Try to lift one. (And that is with a lightweight nursery soil mix!)

1) Root prune no more than 1/4 to 1/3 of the way around the plant every 2 months. This means using a shovel and making a trench around part of the plant, cutting through the roots in that section. Backfill the trench with loose soil or leaves. At the same time, prune the top of the plant. You could thin out the branches, but leave some tall, or you could cut all of them somewhat shorter. Remove about the same amount of top as you have root pruned.
2) After 3-4 sessions you will have cut a circle all the way around the plants. The top parts have also been reduced in size so the reduced root mass can still support that amount of top. Now start undermining the plants. This is probably the hardest part. Very difficult to dig under, but keep the root mass intact. Be very careful as you uncover the new root growth in the trenches all around the plants. Keep the new roots moist, perhaps with burlap sacks while you are working. As you undermine the plant work a heavy duty tarp under the plant.
3) Prepare the new holes. Make them wider than the root mass, but no deeper. A bit shallower is better, so the plants end up on a very slight mound, never any lower than they are now in the ground.
4) Have enough people available. Lift the tarp, carrying the plant to its new location.
5) Plant them as you normally do for your area.
If they are in a full sun area, and you are doing this in the summer, then you might want to provide some shade for a while. (I would not do this in my area in the summer- way too hot and dry, but in WA, anywhere in the rainy part of the state it should be fine)

Rhodies are very shallow rooted, and I think there is a very high chance of doing significant damage to them if they are near the plants being moved. Arbovitaes tend to be a bit tougher, so they are more likely to be just fine.

Here is another thought: If the Viburnums grew that fast, why not just buy a few more for the other location, and prune the existing ones as hard as needed to keep the Rhodies in full view when they flower. IMO Rhodies are a lot more valuable than Viburnum tinus.