OK so heres my take on the situation. The tank is really immature exp. for something that will become really teritorial like a tang...wont allow any other fish to enter its domain further down the road usually, as well as a dirty and messy eater like an eel. The lack of LR in the tank is very concerning, when in combination with 2 emperor 400 biowheels as your filtration. That isnt nearly enough filtration imo to run a 100 gallon tank. the coral (although im not sure what a destiny coral is?) is secreting its zooanthelle...the brown stuff. this occurs when it is really stressed...due to the nitrites being high. With The addition of these 2 fish and coral to such a young tank and underfiltered one (again in my opinion) didnt allow for the cycle to fully occur which is why you still have nitrites that are detectable. Also the only other level you gave was pH but not a value, i realize it is off the chart so how can you get a value right? well what is it higher than, are you using a low range ph test kit from a freshwater kit and its higher than the 7.8 on there or are you using a high range pH kit and its higher than the 8.whatever on there. The levels are still rising due to inadequate biological filtration which isnt allowing the nitrite to be properly converted to nitrate. I would advise getting the coral and fish out of the tank and let the tank set untill all the levels get to where they should be. In the process upping your filtration cappabilites if possible through both addition of LR and a different filter sys.