"But you had to have been scared. The day they said, Piers, it's over." Would there be a difference between "had to have been" and "must have been" in the sentence?
Have to have V-ed (as a finite VP) refers to events viewed as completed in a present time frame, while
had to have V-ed refers to events viewed as completed in a past time frame. Thus e.g.
You have to have been here before, otherwise how do you know your way around so well?
You had to have been there before, otherwise how did you know your way around so well?
On account of the origin of 'must' as a past tense form,
must have V-ed can generally be substituted for either, hence the semantic equivalence of the above to
You must have been here before, otherwise how do you know your way around so well?
You must have been there before, otherwise how did you know your way around so well?
However, being exclusively epistemic in sense, m
ust have V-ed is naturally more limited in scope than the other expressions, which can also serve deontically, e.g.
I have to have paid the bill in full by next Wednesday at the latest, or they'll cut off the electricity.
which may not naturally be rephrased as
?I must have paid the bill in full...