Here's another pic

What does a good reliable soil test say about the soils pH and major nutrient levels?
How much organic matter is in that soil?
How well does the soil drain?
How well does the soil retain moisture?
What kind of life is in the soil?
Contact your counties Cooperative Extension Service office about having a good reliable soil test done to start determining what needs be done to help that lawn.
You could also use these simple soil tests
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
to learn more about the soil that grass is trying to grow in. All plants, grass included, need a good healthy soil to grow in to be a strong and healthy plant.

Here is a link that might be useful: Alabama CES

I am not an expert, but would consider what kimmsr said to be valuable advice. Have you tried raking away (with a good hard metal rake) all of the dead grass, etc, overseeding, and throwing down some milorganite or something similar when you overseed? Raking away all of the dead grass, etc will allow the grass seed to reach the soil. Also using that same metal rake will allow you to loosen up the top of the soil to allow the seed to not just sit on the surface. Then you will have to make sure that the grass seed stays watered for the recommended time period after. This might take a good amount of sweat labor to get the dead vegetation raked up, but I am not sure how else you are going to be able to get rid of it to be able to start new grass there otherwise.

Is now a hood time to do this? Also, where can I find zoysia seed?

Now is the time to do soil testing.
I am not aware that Zoysia seed is sold, everything I have every seen about that grass is that it is sold as plugs.