My filter actually does use activated carbon in it. I have an external canister filter.
I've been trying to restrict the lighting, but I can't do it too much because of the turtle's need for it. On hot days, I leave the basking light off completely, because the basking area has been warming up enough on its own. I've actually only been turning on the UVA/UVB light about once every other day for limited hours.
I haven't been feeding the fish at all.

They seemed to be doing fine just eating the turtle leftovers (and their own babies), so I just stopped feeding them.
Part of the problem I think I am having is that since I moved, my tank is no longer indoors. it is now in a type of enclosed patio room....so it is protected from all the elements, but not climate controlled.
I'll have to look into what types of plants I might be able to use. It'll have to be something non-toxic to the turtle, that the turtle isn't going to just eat all up in a day.
I looked up algae just now to see what plants might help, and I discovered there are tons of varieties of algae. I guess first I need to figure out which type is taking over?
Thanks for the help Boanerges......I guess it mostly helped me realize how difficult this problem is really going to be to try and solve.