Ok this is good info to start with.
My first concern is that you get an ammonia reading. Although very low and shouldn't be toxic, but that worries me. Can you double check that?
If you are getting some ammonia with your current fishload, you may be getting spikes when adding new fish. BUT, why would only the new fish be effected and die? Doesn't really make sense.
If you are getting some ammonia, double check the flow in the tank and make sure detritus is not building up anywhere. You are on the lower side for LR as well (I run my tanks the same way) which is fine but perhaps adding a few more pieces of cured LR might add enough bacteria to get rid of that ammonia.
Having said all that, I don't think thats the problem.
Do you see any stress to the new fish caused by the old ones? Does the Tang bully new fish?
Oh and by the way, for that lateral line, make sure you feed that tangs lots of nori and vitamin soaked foods. They can recover from this with some time and care. Don't know how long he has had it but it can/will get better.
Keep adding more and more info about your tank as it comes to mind. Even if you think its silly, something may come up.
I hope things turn around for you...its a weird situation that only new fish die
