Just keep the lower branches pruned off. Be sure to make cuts just outside the branch collar.

Limbing up a tree to expose the trunk is a perfectly acceptable form of ornamental pruning and is often performed on Natchez.

Limbing up is not what I'm trying to do. It's more like limbing down, if that's a thing. I understand that the Natchez will grow tall, and the ones I've seen begin their leafy branches well above 4 or 5 feet. I want to bring SOME (not all) of the branches down so that the leafy branches offer privacy beginning at 4 or 5 feet from the ground. Hope that clarifies my intent a bit.

Natchez Crape myrtles develop a wonderful umbrella shape. And they naturally put out more trunks than other myrtles. The trunk density can be considered a form of screening. And the overarching canopy of the tree means that leaves will be hanging down to six or seven feet.

The 'limbing down' method really does not look good. (I'm assuming you mean lopping-off large branches, for a 'layered' look)
In fact, there's a name for it: Crape Murder. Here in Madison, being a Crape Murderer is equivalent to chewing gum with your mouth open. People will shun you.

I suppose, considering that the trees are young, one could clip the outer tips of the branches, regularly, in the way that one shapes and maintains a hedge. That would be quite a chore, though.

Me, I'd leave the Natchez totally alone, and let them develop their own architecture. And I'd underplant them with Magnolia Grandiflora, Glossy Viburnum, or a Clumping Bamboo (the kinds that don't send out runners).

I wish you'd asked us earlier. There are other Crape Myrtles that assume the dimensions you're describing, all by themselves. Acoma looks like a miniature Natchez, except that it blooms more. On the more mature specimens I've seen, the leaves start at four or five feet - naturally. And I think Catawba would also grow within your desired dimensions.

Again, I think that simply leaving Natchez alone, with no pruning at all, will allow it to develop the exaggerated umbrella shape which would yield maximum screening.

However, aside from getting precisely the screening effect you'd envisioned, I'm guessing that you chose the right plant. A majestic tree like Natchez, if allowed to develop its own natural architecture, will give your property a scale and an aura that would be hard to match with another plant.

I know nothing about these trees so take this with a grain of salt. Would mounting weights on the lower limbs cause them to bend down closer to the ground? You could large water jugs to make it easier to control the amount of weight. Maybe make them look like hanging baskets around the lower rim of the tree. Once the limbs are formed the weights could be removed? Just and idea....