Curator,
I have a BioCube 29, so I understand some of the issues. As you can see, there is a wide variety of opinions about many reefkeeping issues. I'm not saying anyone is wrong or anyone is right. There are so many variables in this hobby that one person's experience may or may not apply to you.
Anyway, I'll tell you what I do with my BioCube, and you can take what you like and forget the rest.
First, as you have discovered, tap-water causes problems. I bought the saltwater for my BioCube for about a year before making my own water. Changing 5 gallons every couple of weeks is managable with bought water in my opinion. Because the BioCube does not have a skimmer, and is a small water volume, regular water changes are very important.
Second, make sure you top off with fresh water (RO/DI filtered water bought from the same place you buy the salt-water would be appropriate). The water level in the 3rd chamber (the one with the pump) is supposed to vary with evaporation, but especially now that the humidity in the air is low you may have to top off every couple of days to keep the water level between the min and max lines.
Third, I recommend you make your own filters. The Oceanic filters are expensive and clog easily, further exacerbating the water level issues in the 3rd chamber. I use some generic filter pad and Purigen (inside a fine mesh bag) to create my own filters. The Purigen is a resin that removes organic waste from the water. I find that it helps keep nitrates under control since we don't have a skimmer on the BioCube.
Finally, I found that additional flow has helped too. I bought a Koralia Nano powerhead a few weeks ago and have really noticed improvement in the tank. They are not expensive and are quite small. Of course there are other small powerheads that would work as well.
My opinion on the bio-balls is that, while not ideal, they are not as bad as some people make them out to be. They do improve oxigination of the water, and they do a great job removing nitrites. They can cause nitrates to rise if you allow them to get dirty. I do two things to prevent this. I always make sure the filter is installed so that the water is mechanically filtered before entering the bioball chamber. Then I clean about a third of the bio-balls every few months. I just put them in some salt water and scrub them a little. Don't clean them all at the same time or you could cause the tank to cycle.
I hope that your experience with reefkeeping improves and becomes less frustrating. I certainly know how you feel, as the BioCube was my first tank as well.
I forgot to mention, but you did add a heater, right? The biocube does not have a built-in heater, and you'll need one this time of year.
Karl