If your pond is not currently getting a plankton bloom, and it sounds like it's not, you might try fertilizing starting in March or April before the FA gets going well. If you get a bloom going before the FA gets cranked up, the bloom will entirely prevent it from growing because it cuts out the sunlight penetrating through the water. A not-insignificant side benefit is that your fish will grow drastically faster because phytoplankton are the foundation of the entire food chain in your pond and when there's more plankton, everything else on up the food chain, from zooplankton that feed on the phytoplankton to insect invertebrates to fish fry etc., grows faster as well, most importantly your fish.
I do know of a lake that has had tilapia stocked in the recent past and never has an issue with FA, but I also know of a 1/2-acre pond near me that has an FA problem and was heavily stocked with tilapia last year, and they didn't even make a dent in it. So they're not a sure thing. But they do provide a lot of forage for your other fish, so that's an upside even if they don't control the FA.
You might just try both. It would make for some happy fish.