Confusing double occurrence of Past Perfect in the same sentence

Context is everything, resistance is futile:

That little word so indicates something happened before the two things mentioned in the sentence:

1. The afternoon had been very hard as many candidates showed up. So, before the young man had had a chance to say anything John had given him an application form.

2. The candidate spoke for five minutes without stopping. So, before the young man had had a chance to say anything John had given him an application form.

Without knowing what precedes the "so", I would eschew calling it in favor of the simple past. The answer is that it depends on the broader context. A broader context, called a co-text by some linguists.

One can easily imagine that the two activities with the past perfect precede the action in the simple past of the first sentence. Why not? It's perfectly possible.

Naturally, in another context, one can also write:

The young man was late and before he had a chance to say anything John had given him an application form.

The takeaway is this: context can come in a preceding sentence and is not always at the level of a single sentence.

In your proposed alternative, the remaining past perfect sounds wrong. If you’re going to remove the first, you have to adjust the second too, like so:

So, before the young man had a chance to say anything John gave him an application form.

The reason you might not want to do that is if the relationship of this sentence to a larger context required the past perfect. In that case, you have to put the whole sentence into the appropriate tenses for it to read right.

Nested tenses that orient the reader regarding time and order of actions need to be balanced, else they end up disorienting instead of orienting, much like nested parentheses must be balanced to make sense.