I'm a little biased here since I sell them, but I think Blue Tilapia would be a great answer to your forage, weed, and especially the blue/green and Filamentous algae problems.
The addition of Blue Tilapia would provide plenty of forage for all predators mentioned PLUS be a forage for small predators such as Bluegill. If your lake has nice sized Catfish in the 10+ pound range, you would most likely never see a dead tilapia in the fall. Every fish except the tilapia would go into winter much healthier for the following spring spawns.
