Although you test 0 phosphates the tests don't test for organic phosphates. Your macro alge is helping. But there is phosphates and nitrates and light. Reduce one of these and it will reduce it. Changing or adding gfo could help but don't know what you have or have done.
Using the slime treatment is treating the Symptom but not the cause. Would take the slower approach. To treating the cause. And only use the slime treatment in concert or as a last result.
I have had best luck ridding cyano with increased flow in area of problem, reduced light period and addition of more hermit crabs and cerith snails. Good luck!