This is my opinion as an American. The past perfect is not gone, but it is my impression that we don't use the past perfect when the simple past is sufficient to relay the intended meaning. Most of the time, as in your sentences, there are other constructions to supplement the simple past and convey it as perfect past.
I heard about her before I met her.
The temporal marker "before" supplements "met", turning this simple past into the past perfect. But the following certainly wouldn't sound foreign to an American.
I had heard about her before I met her.
or, using the contraction...
I'd heard about her before I met her.
As for the following...
Yesterday, I heard about her for the first time.
This isn't past perfect. It's simple past, but an American might say the following.
I had heard about her when I met her yesterday.
Without the temporal marker "before", the past perfect is essential to convey the meaning. However, for that sentence to sound natural, I'd have to hear it as a response to a question, such as, "Didn't someone tell you about her?"
As for the following statement:
By the time he got to Phoenix, he had had enough to drink to make him stagger.
This is something that Word will fuss about and I'll ignore or modify to mollify. Word isn't the expert; it's a tool to help those who aren't. If you're an expert and Word is catching stuff, either it's wrong or you're too tired. An easy way to modify the above sentence and more closely resemble how I would actually speak it is to use a contraction.
By the time he got to Phoenix, he'd had enough to drink to make him stagger.
On the other hand, you can turn the verb around.
By the time he got to Phoenix, he had drunk enough to make him stagger.
The past perfect isn't gone in American English; we don't always use it when we don't have to.
Best Answer
There is no difficulty. The sequence of events in the first is (1) speaker sees documentary, (2) speaker and others visit the ‘Whydah’. One event happened before the other. The same is true in the second example: (1) Drake works for the British Navy, (2) he becomes a pirate. Before is required in both sentences. You can’t write two clauses without linking them in some way, and before is the appropriate conjunction in each of these cases.