People wax rhapsodic about Mr. Neil--"Old School," "real Mafia," "loyalty above all"...bla bla bla. If he were all those things, he would have given up Quack-Quack and Gotti for all the reasons you said. He didn't. Why? Maybe because, even though he accepted Castellano as Don, he resented him and didn't want to bend over backward to be helpful. Quack-Quack was his nephew, and I guess in this case blood ran thicker than water. Gotti looked up to Neil as a father, and I suppose Neil felt the same.
But in the Mafia, you can never go wrong following the money. Ruggiero and Gotti were dealing drugs, and no doubt they kicked part of their earnings up to their capo. And, maybe--just maybe--those tapes that weren't turned over to Castellano had some talk of Neil's share--meaning that he could have been in mortal danger if the tapes had been turned over.
From what I've read,Neil is actually taped telling Angelo to turn over the tapes. He berates him by saying that Ruggiero doesn't understand Cosa Nostra.He tells Gotti that Paul keeps breaking his back over the tapes and that,if Angelo keeps stonewalling,"we might have to roll it up and go to war". He also warns Quack-Quack ,that should it come to that, a lot of people could get hurt.I would bet that there's nothing connecting Neil to any drug business on the tapes. If there was,nephew or not,Cosa Nostra or not,Angelo would have a life span calculated in moments.