Google earth...how it looked before my house was built..
 

The red stuff is clay fill dirt. It packs down easily and water stands too long. I water alternate days from neighbors to lessen perpetuating swale problems.
The corner lot where trucks parked nearby had to be specially aerated and top dressed. Top dressing with black kow or other organic material is always a good idea.

But, when you get Lloyd's expertise, you will know what the real issues are. Also, you might want review zoysia care by googling uf site for it. Much of it I see is scalped..Also, with grass that is fairly established letting the lawn dry a bit between watering will encourage root growth. Best fertilizer is 8-2-12.

Irrigation consultant?

Yes. Didn't know they existed either, but he checks the lawn, the sprinkler heads, the settings, looks for leaks and checks the "weather station"---cost me $25 and $10 for one new head. I send you a PM with his name and number if interested

In The Village of Lake Deaton area it was Army Worms last spring/summer that caused a problem with a lot of lawns. I had never heard of them. I have had Mole Crickets in the past (not in The Villages) and they are problematic also - the first evidence is dead grass, usually in circular patterns. Pesticides are your friends.

2nd most important thing next to water... pH

If the pH is off by much from the "comfort" range for zoysia, micro nutrients will not be absorbed. No matter what problems you find and fix with your sod, test your soil and manage your pH to get the most out of the fertilizers and water you use.

The average pH I have found testing in TV is around 7.2, a bit alkaline for zoysia. I would test a 10 x 10 with a light coffee application. if you see improvements in the following couple weeks... treat everything.

Bad Sod
 

I have the same problem exactly as you described. My phone number is 269 317-9175. Call me.