Did you read the article? The only reason there are so many of those sea stars is because fertilizer runoff is providing them a ton of excess nutrients.
I think you need to do both. The sea stars will continue to consume the coral until the problem is solved at the source, possibly for a long enough time that the reef is consumed in its entirety.
No offense, but why do you think you can come up with a solution after thinking about a problem for maybe 10 seconds, when tons of smart people are working on this problem and can't come up with a great solution?
The problem with fertilizer run off is that it penetrates the ground, travels very slowly, and leeches into waterways. Once the fertilizer and contaminants are in the soil, they move very slowly. Like a meter or two per year. So, right now, we are seeing fertilizer and contaminant runoff entering streams, because a farmer in the 1970s fertilized a field that was 50 meters away from a river. I don't think we have a time machine available to go back and tell them to not fertilize their fields, which is basically the only way your solution would work.
The other alternative is to wait it out, but the coral reefs will be gone by then, because they will have been devoured by the sea stars.