To see lots of small minnows is typical and sort of supports the idea that you have few preditor fish, like bass and bream, that can eating them. Chances are that they are few if any because of the poor oxygen conditions. The duckweed blocks oxygen diffusion from the air and there is no phytoplankton to produce it in the water. Being in S. Miss., the high temperature in the summer causes rapid oxygen depletion. It is fairly easy to determine what you will need for aeration. Do a search for Aquatic Ecosystems and they have plenty of information to help you determine what size you need. Also, I deal frequently with Stoney Creek in Michigan which I find has very reasonable prices. Just about any company that sells these systems can help you spec it out but you will need two things. Determine the area of the pond and the average depth. Also figure out if you have any deep holes and determine the depth.

If you have deep hole you will be able to get by with a smaller system. For a one acre, expect to spend about 500 to 700. Two acres may run as much as 1500 depending on the depth to area ratio. One other thing. If you are good at rigging things, you can try to build your own system. I can tell you from experience that this usually turns out to cost almost as much as a package deal. Do a little research and determine what you need then then shop around and determine if you can afford it. I can tell you that you the investment will be worth it. Within a few weeks of aeration you can at least restock the pond. By the time they grow you'll probably see improvement. Whether or not you need to dig it out absolutely depends on the pond architecture. Figure this out first then decide what the next steps are.

Take a boat out and start probing around and when you get a better idea of the depths you will be much better equipped to spec it out for aeration. If the pond averages out at 4-5 feet and has some deep holes at 8-10 feet you don't have to drain and dredge. You have plenty of volume and you just need to work on restoring what you have. Digging it out will cost you several thousand but aeration will be a fraction of this. Do a little more research and see what you can come up with.