Why should spraying and biological control be our only options? HN has had a bunch of stories lately on using CRISPR and gene drive to render entire populations infertile. Let's do that here and make this species extinct.
You do have an argument about ecosystem cascades and food chain disruption inveighing against arbitrary extinction of pests, but we should evaluate these things on a case by case basis and not just assume that any species we eradicate is "load bearing". Many species aren't.
Edit: relaxed claims.