How about a mixed hedge with both evergreens and deciduous shrubs? I don't know where you live, but here in the mid-Atlantic, camellias are evergreen as are Kalmia latifolia (mountain laurel). Both will reach a good height over a couple of years and both could be pruned if they get too high in 20 years. You could include azaleas and maybe some small trees such as Serviceberry and some small magnolias. Do you need to dampen the noise year-round or mostly in the three seasons you are outside? The best way to to that is with plants staggered along the lines so they will be overlapping once full-size and perhaps three deep (but not in a row, if you know what I mean). I think it is prettiest and best with a variety of types to guard against disease or pests taking out the plants if you have only one type planted. To a certain extent, being patient offers great rewards. Neighbors who have planted trees to create an instant hedge often end up losing many because they become too crowded. I am now watching trees die back at two houses around the corner from our place. The staggered planting allows for air circulation and root growth. It is also much more interesting to look at!

One shade tolerant large shrub is Florida anise - Illicium floridanum is the name. If you planted 3 gallon ones, they would be 8 feet in about 3 years (most plants do the sleep/creep/leap growth thing). They like good moisture so they'd need to be watered well and mulched. Other shade-tolerant ideas are Carolina Cherry Laurel and Hemlock. All these things are available in 3 gal and larger sizes at Buck Jones in Woodstock (on Hwy 140 going north from Crabapple about 8 miles). A non-native idea would be Aucuba japonica. However, with such a narrow space and having to plant under oaks, I'd also consider non-planting solutions because sometimes plants just can't be the answer - they take time, especially in the shade. Could you build a pergola and train vines on it? Carolina jessamine is a fast growing evergreen vine with yellow flowers in the spring. I understand that you could not build a 15 ft fence, but you might be able to build a tall pergola/arbor. This would allow you stay inside a fixed width as well.

If you are looking at a maximum height of only 6-8', then you are looking at shrubs, not trees. 'Full privacy' typically means evergreen and I am unfamiliar with what broadleaved evergreen shrubs are best suited to your area. However, a mixed shrub 'hedgerow' type planting that includes both evergreen and deciduous plants will provide excellent (if not "full privacy") screening plus offer extended seasonal interest as well as wildlife habitat. And eliminates any 'gaps' that could occur from the failure of a single plant in a monoculture hedge. Since you have a mixture of light conditions, that broadens the selections available. I would consider rhododendrons, pieris and kalmia as evergreen suggestions (possibly boxwood or Japanese hollies also) if sufficiently hardy, mixed with fothergilla, hydrangea, spirea, clethra, shrub dogwoods and dwarf lilac for the deciduous components but the choice is up to you and there are almost endless possibilities. Also, dwarf conifers could be included as well.

Wax myrtle could be a good option in your area if soil is neutral or acidic. Many culinary/(folk?) medicinal uses and I don't recall hearing of any toxicity issues for children or pets. Nursery person should be able to confirm. Loropetalum is another that might work. Most of the newer named cultivars will be smaller than what you're looking for. But the unnamed varieties found at the big box stores can usually make a large shrub or small tree. Major ice storms can be hard on these, but are pretty good about recovering.