Nusiance algae, diatoms, cyano all need 3 things to live. Water, light and food. Take away any 1 and it dies.
We can't remove the water, so light and food. If you want coral, you need the light. That leaves food....nitrates, phosphates, silicates. By using tap water, you are adding food everytime you add water. You can run GFO (yes yote, Rowaphos and Phosban are GFO, just more expensive than the GFO from BRS), but it will be costly. GFO isn't cheap and you would need to replace it at least every 2 weeks if not sooner. Your best bet, and cheapest in the long run is an RO/DI unit.
Like everyone said, just yank as much out as you can and stick with a good mantainence schedule.