Ohio Scott, plants are a much trickier group to work with than are fish. A plant that works great in one area, might be horrible in another. This means you really want to get local advice in addition to what you get here.
Probably, some type of plant will grow in your water 3-4 ft. deep and less. When I say grow, I mean fill in completely. Water lilies aren't invasive here but might be in your area. I also personally like the various species of bullrushes. Splatter Dock (Nuphar lutea) aka yellow water lily might not be invasive in your area. These are all emergent vetetation.
Almost any submergent vetetation can become invasive. The best waterfowl species, by far, is Sego. However, it certainly can foul a fishing line.
Most people will tell you that the best way to control vetetation is with water depth. You seem to have done this. Keep us informed.
