Your idea would work, but you really don't need the height of Italian cypress. Instead of lining the back fence length with them, you could do something like using 3 at the corner (L-shape planting scheme ... even though my picture does not illustrate it well!) in order to add punctuation to the yard, and then continue with ERC. Presumably, you would mark the opposite corner of the yard with IC, too. It would be a serene, formal-ish look, if that's what you're after.

The wall is very attractive and personally I wouldn't want to hide it. Small trees could be pruned up so they screened above the wall height but allowed the stonework to be seen. Perhaps a mix of evergreen accents and small deciduous trees?

There is nothing "natural" about a row of Italian cypress or any other tree planted in a long, narrow row. 'Natural' would connote a mix of various native (usually) plants - not a single species - planted in a very loose and free-form pattern. Is that what you want or is the focus really on privacy, natural aesthetics be damned?

btw, I second floral's opinion that the wall is very handsome and doesn't deserve to be covered. Many shade trees limbed up to an appropriate height would provide more than adequate privacy during summer months but leave the area somewhat exposed in winter. An exception would be something like the fastigiate European hornbeam Frans Fontaine, which has a very dense and upswept branch and twig pattern that provides a decent amount of screening even when out of leaf.

People so often automatically design to the perimeter for a screen. Sometimes that is the only solution, but often it is not. Sometimes the placement mid-garden of a full tree with a spreading crown blocking the sight lines between house and fence is an effective enough privacy screen. That allows for more attractive beds along the back with greater flexibility for varied plant choices that will also contribute to screening, but not look like a green fortress wall. Kind of depends on your taste.

Who owns the metal railings? They'd be perfect for vines if you are allowed to grow things on them.

A row of Italian cypress close together does look more like a fortress wall than like a natural woodland scene. There are a lot of them around here and Fort Cupressus is the vibe they provide. A mix of small (10'-15') evergreen, densely foliaged shrubs of different types limbed up eventually to show off the beautiful wall would provide a more natural look.

It isn't just a matter of blocking everything, but that line of sight, as mentioned above, and also providing a focal point other than what is currently grabbing your attention - which is the neighboring houses and other objects in their yards. A few well-placed groupings of trees and shrubs will go a long way to give you a greater sense of privacy in your own yard, and much more aesthetically pleasing than a wall of evergreens.

Let's suppose a god could swoop through the neighborhood and solve the screening problem without regard to property lines, just screening where screening would best be. Without question, he would put it at the TOP of the retaining wall because that's where it would physically work best. A hedge only half the height would be as effective. So too bad, J. Sean, that your surrounding neighbors aren't the ones interested in screening you out, as they could solve your problem with you doing nothing. (Before commencing with a plan, be sure no neighbors already have a plan to do this.) I completely "get" others' point about not hiding the stone wall. but trying to screen and preserve view of the wall means that one must allow tree canopy to hang low at the back side, or one would be focusing periodically on the neighbors' feet. So that's not ideal either. Given that the tree canopy area would be at the neighbor's first floor level, they're going to need to trim their side of the lot line like a hedge, or allow the tree to consume space in their yard. It's likely they would sabotage this effort, and eventually, there would be no canopy allowed at this level, on their side of the fence. I know it would not work for me if I was the neighbor as I am fairly obsessed by controlling what happens on my side of the line.

When the OP said he wanted to create a "natural screen," I think he was using the word 'natural' to denote that the screen was made of a natural material -- like a dog, tree or rock is natural, regardless of how these things are employed. Given that he was speaking about a hedge of only two possible kinds of plants, I don't think he was trying to describe a screen that attempted to look like a screen only as nature would have created it. It seems some automatically recoil in horror at the idea of a uniformly smooth "wall" made of green foliage! I don't see it any differently than if one unearthed a rock from the ground, polished and incorporated it into a precious metal setting ... and then called it a gemstone. Using plants in highly controlled manners in order to create "architectural" forms is not a horrible thing in my book. In fact, it seems a higher calling, to me, to use materials in ways refined exclusively by man. To argue otherwise seems like asking for the bark to be put back on all the 2 x 4s. With exceptions, of course, much of real nature in the plant world is just a weedy bramble patch. The "mixed shrub" borders that so many promote do not really look like real nature, though they look somewhat naturalistic. In some cases, such borders even evoke images of Candyland! I hope we don't get to the point where using plants in an architectural way becomes labeled as racist or xenophobic, but I can almost sense this coming.

Pre- built privacy panels would be the easiest.

There are a lot of different styles available with variations of print/ cut and visibility.

http://www.exoticpebblesandglass.com/products/outdeco-privacy-screens/