Patrick Vincent Casali has written a long article (Opera Quarterly 13 (4): 77-91, 1997) detailing Puccini's intention that his opera be pronounced Turando[t]. Here's a 1962 interview with the Met's John Gutman and Rosa Raisa the first Turandot:
GUTMAN: In addition to being the very first Turandot, I know, Mme Raisa, that you appeared in other world premieres and several
American premieres. Would you tell our audience, please, what some of those premieres were?
RAISA: My pleasure, Mr. Gutman. In addition to Turando[t], which is pronounced the way I pronounce it and also [the way] it was
pronounced by Puccini and Toscanini, so, [therefore] it is really "Turando[t]," not Turandot!"
GUTMAN: [taken aback] Thank you very much, Mme Raisa. This interests me very much. I know that this has been a controversy for a long time and . . . ah, we certainly take your word for it, since you were the original Turando[t].
RAISA: Thank you.
Listen to the interview here:
Here's another with Robert Lloyd and Dame Eva Turner a famous Turandot who was at the opera's first performance.
LLOYD: Dame Eva, there's one little problem we have to solve before we can have this conversation.
TURNER: Yes?
LLOYD: I've noticed that you say Turando[t]."
TURNER: Yes.
LLOYD: And I say "Turandot." Can you explain why?
TURNER: Yes. Well, because in my day it was always "Turando[t]." And you see, I was at the first performance that Toscanini conducted, and [pause] it was "Turando[t]." And whenever [sic] I sang it for the first time, or whenever I sang it, I say "Turando[t]." And, I think I have to confess, I like it. More especially when it involves a musical line, to keep the continuity going. It isn't quite so chopped. But of course, it isn't quite so Chinese [laughs].