Hey, this thread is a week old, but I'll post anyway. I'm running the jbj nano-cube myself, and have beaten the nitrate problem finally (knock on wood). A few things I can offer:
The stuff you bought is either amquel or novaqua, both products made by Kordon. I would personally stop using these as an ammonia/nitrate remedy, because they just 'lock up' these toxins and don't physical remove them. Also, once they get chemically saturated, they have been known to suddenly 'release' all of what they had absorbed, doubling the problem in your tank. Additionally, this is a quick fix solution, and doesn't really address the problem of where the toxins are coming from.
That being said, your nitrates could be coming from a number of places:
-You may have overstocked your tank to begin with (not sure from what you listed). The tank is only 12 gal., and it's hard to not put many fish and corals in. From your list, I think this is what happened- how many fish were there?
-You may have been overfeeding the fish and inverts, and excess food could have converted to nitrates. You said you don't feed them too much though- are you feeding your corals?
-You may try doing some larger water changes if you can do it without disturbing the tank too much- maybe 4-5 gallons?
-The filter system may not have been functioning properly. With all that rock, I think this is unlikely, because you should have had plenty of good nitrifying bacteria in there already. I'm assuming the rock was fully cured when you added it? As for the actual filter in the tank, those black filter sponges should get rinsed regularly to get rid of any detritus that is decomposing. (Try and keep one over the intake on the upper left side, so water has to flow through it to get to the filter box. If you do that, the rest of them shouldn't need to be rinsed, but doing that I know mine gets pretty nasty if I don't rinse it.) As for the rest of the stuff in there (ceramics, bioballs, etc.), leave it be so the bacteria will grow on it.
I keep mine even purer by doing regular water changes (2gal./week) and keeping some feather caulerpa. This is a good-looking macro-algae that should be available at your local fish store. It's been really beneficial in absorbing the nitrates that the fish produce and supplying oxygen to the tank. I recommend reading up on it and then considering some sort of macro-algae for your tank. There's probably some good threads on this website.
I guess that's about all I've got on this subject- sorry about the really long post. I'm not a PhD, but I've been in the hobby about 10 years now, so I'm confident this is good advice. Anyway, if you have questions, let me know, and if you think of anything else to post, please do. Good luck, and don't give up!