At the end of the day it is your call. I think you are looking at this the wrong way. We shouldn't look at our tanks and think which fish can I cram in here and survive. I think we should look at our tanks and ask ourselves what can thrive and live a full, happy life in the tank.
This is debated some, but many argue that a stressed fish fights off disease less efficiently. The reality is that there are probably diseases in a lot of tanks, but fish are healthy enough to fight them. Other than that, I am not a tang expert, maybe
@4FordFamily can give you some insight on the downside of having a large tang in such a small tank and expand on my post.
Also, a Moorish Idol is quite a large fish for your system as well. Is that fish still alive?