Crossvine - Bignonia capreolata
Carolina jessamine - Gelsemium sempervirens
Jackson vine - Smilax smallii
Armand clematis - Clematis armandii

The first 3 are native, the clematis is not.

I have considered both crossvine and jessamine, but was really wondering if there was any way to get complete coverage from top to bottom. I know that the jessamine will be leggy at the bottom and tend to cover the top only. Is the crossvine also very top-heavy?
I had also thought of climbing hydrangea, but I basically know nothing about it.
Do you think that if I was diligent about weaving either crossvine and/or jessamine where I want it that it would give me that coverage at the bottom I'm desiring?

I like confederate jasmine.

All of them will tend to lose leaves at the bottom. The way to overcome that is to prune some of the vines back to the ground every couple of years, forcing it to stay nice and full.

"would give me that coverage at the bottom I'm desiring?"

I would consider Carolina jessamine and Confederate jasmine. For me, I have been happy with the results of only putting in some effort to rejuvenate the plant by pruning back the over growth. The plant showed a response to this method by springing back healthier and filled in the area vigorously.

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