Hey Jnarronecu, Welcome to BP. Lot of great info here as you may have read. I would reccomend getting the Perfect Pond want one book read it and continue to research until you feel a bit more comfortable with what you want to do.
But just for some Ideas from my looking at your pic's and what you wrote, I would say this. It might be good, if your pond(s) holds water do not mess with it and consider it or those a brood ponds as a management tool for a larger 10 or 15 acre lake that could help same some money when stocking day(s) come plus you may be able to grow out some FHM/CNBG/or other fish for that matter.
If you have a site and it appears you do for the big lack you could dig a pond of 1/2 to 1 acre that is feed from the runoff of the others until you build the big one. A well could feed the smaller pond area and hard plastic pipe to the others or the larger pond/ Lake to control water/fish etc...
Core samples will help you a lot as suggested and the existing ponds may serve a purpose even though they are shallow, and as some here will say "IT DEPENDS" and it does.
You found a great place to start hear and a way to not only save money but a bunch of headaches if you read through many of the problems that others have had and solved here.
Good luck and welcome again. FYI I am just a novice and offer opinions only. East TX and NC are two different for me to make a lot of particular suggestions on fish.
