There's no good solution for killing the moss (algae) that I know of that won't affect the bloom.
Phycomycin, Green clean type products, or your copper based algacides are some of your choices. Phyco was developed for treatment of blue-green algae in an aquaculture environment, and is supposed to be used on newly growing algae. It doesn't work so well on floating mats.
Since algae grows so fast, I think once you kill off the weeds and have the unused nutrients available, it'll be a race between FA and the bloom to see who wins. Hopefully the bloom will get started, and limit the FA to growing where the sunlight reaches. I also hope that the bloom doesn't get too dense with all the available nutrients once the weeds are gone.