Oh dear ... I know that feeling in the pit of your stomach when you look at the place where the tree was!
By now you are used to not seeing the trees and have started to look at the bright side of the situation and the opportunity for a new planting. You didn't indicate what type of plant it was that you removed nor the conditions (sun/shade, dry/moist or whether the plants are subjected to road salt when you have snow), so you may want tp consult a local nursery for suggestions.
I understand why you are thinking about the leatherleaf viburnum (large, evergreen) but it is not a plant that is native to Virginia (or North America for that matter). To find a list of plants native to Virginia, visit our Native Plant database and do a Combination Search for Virginia selecting shrubs that will grow to 6-12 feet and then trees in a similar size range. The lists provide links to detailed information pages for each plant. Your choices will be limited if you have your heart set on an evergreen but you will find a number of interesting and attractive native plants that usually offer a wildlife benefit (nectar for butterflies and bees or berries for birds).
I like your idea of erecting a trellis along part or all of the area to be screened. Even a fairly open trellis will block the view enough from the road to give you a sense of privacy and it will give you an opportunity to plant vines (annual and perennial). You can search vines the same way and will find 75 to choose from that are native to Virginia.
Here are a few plants I have selected from those lists. Once you see them all, you'll be getting out your chainsaw to make room for more!
Small Multi-stemmed Trees