Nitrates are definitely an issue with any fish, especially tangs. You need to get these down, ASAP. Unfortunately, there is no product out there that elimates nitrates. The nitrate sponge by Kent does not work well at all. The only way you are only going to get rid of high nitrates is large water changes. I would be doing 30-40% water changes at least once a week.
That diet you have your fish on is not very sufficient. There is really only two nutritious items on it, since brine shrimp really does not have much nutrition at all. You definitely need to get some kind of green matter into the tang's diet as well. Seaweed sheets would be goof for this purpose. I would pick up a few formula foods, such as formula 1 and 2, VHP formula, reef formula, etc. They contain a very high mix of different seafoods, and will provide your fish with a great variety. I would also recommend using garlic in their foods, as well as vitamins like Zoe, Selcon, and VitaChem. Adding vitamins to the fish's food will help reverse HLLE.