Japanese, Chinese, and Common privet are considered invasive plant species in the SE, including North Carolina. As someone who has spent quite a bit of time volunteering to clear native forests of privet, I'll strongly suggest that you come up with other plants.

I also agree. Despite denial, when they mature (and for privet that doesn't take long) there will be distribution whether on your ground or somebody else's. It's a cheap hedge to put in so it's tempting, but there are a lot better alternatives and if you buy in bulk, you can get inexpensive starts much better suited to your locale and needs. Our soil and water conservation districts offer packets of such starts every year and I'm talking about availability of quantities in the hundreds very economically. While your at it, there are also a lot of shrubs who offer suitable habitat and food.

Viburnums might be an option. Witch hazels. I have used blue and dwarf arctic willows occasionally and was please with the results. The dwarf arctic willows should top out about five to six feet and are tolerant of most any situation you can put them in. They'll get as full as they are tall, and are as full on the bottom as top. Standard or blue arctic willows get larger. Three to five years translates to fast growing, btw. Hey, also have had wonderful luck with deutia gracilis. It has the advantage of gorgeous blossoms as well.

There are also dogwoods who would fill the bill.

Evergreen: Japanese holly and Chinese holly grow well here in Raleigh NC, also zone 7. Laurel, maybe a few Camellias tho they are slow growers. Clumping, not running, bamboo. Ornamental grasses. If you don't mind deciduous, Wiegelia is a fast grower and blooms, also the other spring blooming shrubs, Forsythia, Mock Orange. Loropetalum would do well, also Abelia. So many to choose, do a mix!

Chinese privet does make a nice dense hedgerow that grows much taller than 8' here in our zone 7B climate. It is also very invasive. If you plan to plant it under the canopy of your existing wooded area, beware, because if your trees are saplings the privet will take over. The privet does not grow in mowed areas of our yard but occasionally a young shoot will pop up in our garden beds. Once it takes off, you'll have to dig the privet up by the roots to get rid of it and it is impossible to get all the roots. We didn't plant it here, it just grows. One thing we absolutely do love about the privet is the cardinals love the berries and often over winter here. I hope this info helps