Ask Mr. Smarty Plants

Sounds like you have already tried most of the plants Mr. Smarty Plants would have suggested, so maybe you need to go to Plan B. "Shade" is considered to be less than 2 hours of sun a day, and several of the vines you have mentioned should have been able to do well there. So, let's look at the hackberry trees and see if that is the problem.

A number of trees have allelopathic tendencies, meaning they maintain sole rights to the moisture and soil nutrients in their space, at the expense of anything that tries to grow under them. Celtis occidentalis (common hackberry) can spread toxic materials to inhibit other plants in their area through roots, leaves and stems. Thus, low productivity rates and relatively bare areas occur under hackberry trees. It is not a particularly attractive tree, but it is considered a boon to several forms of wildlife, including birds who nest in the tree and eat its berries, and is a larval host and/or nectar source for butterflies Tawny Emperor, American Snout and Question Mark. Besides all that, it does provide shade in summer, not a small consideration in Texas. The hackberry is most definitely a survivor, being able to adapt to many soils and environments and, once established, is well-equipped to hold its ground. 

Just in general terms for your landscape, it wouldn't hurt to have a trained arborist come in and limb up and thin those hackberries. Cutting them down would be a huge project and would alter your landscape probably more than you wish. It would appear you are going to have to find a non-plant solution to your need for privacy. There are products that can be interwoven into chain link fence that you might consider.  Or you might consider replacing the chain link fence with a higher, more opaque fencing. We just don't think you're going to defeat the hackberries.