Nicholas, I second what Miles said. Learn everything you can about beavers and how they make dams. They are amazing, they are some of the best engineers we've got. Some of their dams have lasted for our generations, not to mention their generations.
It wouldn't hurt to get a hydro engineer out there to give you a consultation and some ideas. My dad had the same kind of situation with a creek that would flow at about the speed and volume of your fastest photo, into a pond he dredged out, and he had erosion problems on the sides, almost no matter what he did. He tried to cement the walls, he tried to make rock edges, and inevitably the water cut in behind the man-made materials.
A beaver would have your situation fixed overnight, they are that good! Takes a little maintenance each year to make sure it's holding. Ponds don't just sit there and look great. They are the weak link in a water system because so much is going on in them.
I have about an
acre pond, and the whole month of October is dedicated to Pond Maintenance, when the water is lowest. But I love the pond, and I'll do whatever it takes to keep it.
You could learn a lot from any local farmers who have built their own ponds. In my area there are specific plants that are generally used to help with erosion, berm stabilization. Willows is one of them, and reeds. There are many different types of willows and reeds, and the best ones for your pond would be what is used locally,
native plants. Reeds need maintenance or they will fill in the whole edge, but there are advantages. The birds and ducks will bring pond plants in on their feet, so you'll be finding all kinds of stuff you didn't put there that might or might not be a good thing.