If you are upstream of their ponds, then your pond should fill first!
Two possible problems:
1.) The closer you get to the uppermost slopes of a watershed there is LESS water available. Most waterways in nature exhibit a dendritic (branching) pattern. The farther you are downslope in a watershed, the more branches come together and the more water is available to fill ponds. (Assuming the water was not intercepted upslope.)
2.) Observation bias. Are the ponds around you truly full? If your pond goes down 2', then it substantially shrinks in size in the satellite view due to all of your area of 1' deep water at full pool. If your neighbor had a pond with perfectly vertical sides, it could go down 2' during a drought, yet it would look to be exactly the same size on the satellite view.
The two ponds that are closest are relatively bowl-shaped, so they hold water more "evenly". The one closest to me is 95% full and the other 85%. They were just about dried up when mine went dry last year. (I say dry...mine still had about a 2' of water in a 20' diameter...to me that's dry)
Are there any waterways on your property that transmit water bypass your pond? Diverting that water to your pond would probably be the best way to sustain your pond during subsequent drought conditions.
I don't believe so. It's fairly easy to see where the water runs. There is one area on the west side of my property that appears to be an old watershed. There is a small ravine running towards my neighbors pond, but that eroded area never gets "sloppy" in heavy rains like the area running to my pond, so I'm not sure if water still runs that way or not.
Even if your pond shrinks down from a 1/2 acre to a 1/4 acre during a drought, you could still support a decent fish population. However, if your depth in the deepest parts is only 8' when you go down 2', then you are really starting to push the limits for fish survival during a hot Texas summer. Do you have AC electricity available near your pond? If so, you might read some of the aeration threads. If your fish are in warm 8' deep water that is well aerated, then they should still survive a Texas summer during a drought. However, if your pond is going to go almost dry every seven years due to low rainfall periods, then any fish population development would have to be based on relatively short term goals to make sure you don't waste a lot of money and effort.
So when I bought the place the pond was fairly well stocked. Cast a line, catch a fish. Lots of bluegill and 1-2# LMB. In fact, I reeled in a couple of monster large mouth bass. Was sad when the pond went down so much because I knew I had lost them. Not sure how they did it, but I know that a few fish survived the dry spell. I have reeled in a 1# LMB since then and you can see a few decent bluegill swimming in the shallows.
I actually just added 100 more fish two weeks ago. Doubt they all make it, but it's more of a test right now.
Also, your idea to build a cattle tank upstream might give you double value. It would water your cattle during normal rainfall periods, and you could fence off your larger pond and exclude the cattle and develop that pond for fishing and/or recreation. During a really bad drought, you could then siphon or pump water from your cattle tank to your main pond to save your main pond. You could then give your cattle access to a small corner of that pond to get THEM through the drought.
The large pond will not be accessible by the cattle once the new tank is in. Even if the small cattle tank dries up, I have a well on the other end of the pasture and multiple 700 gallon metal tanks as backup. I like the idea about siphoning off water from the cattle tank if necessary. It would be about 1500' away from the large pond, but would be pumping water downhill so wouldn't be too much strain on a trash pump I don't suppose.
Good luck on improving your property and practicing your rain dance moves!
I'm afraid my dance moves would all but scare off anything around, including the rain.