Learn English – The Correct Usage of Have and Had

The reference date is Friday, September 28, 1894. The specific event on that day is what detective Geyer hopes to find out, namely, that Holmes checked into the hotel whose guest register the detectives are reading.

By using had picked up, we are meant to believe that something happened subsequent to (after) that action. The next sentence informs us

Geyer guessed Holmes and the children had reached Cincinnati later that same day.

Okay, so had reached refers to the same day, Friday, September 28, 1894. And later that same day tells us the had reached Cincinnati occurred after the had picked up in St Louis (or at least this is what Geyer guesses).

But this other instance of the past perfect leads us to believe that some action occurred after had reached Cincinnati.

And this action is the one that the scene is setting up for us: that Holmes checked into the hotel in Cincinnati.

It's a mystery: some suspense is built up in the reader by using these past perfects, but not telling us explicitly what action comes after them. But we can also follow the detectives' train of thought and we can guess that Geyer will find some clue to Holmes's checking in, which he does. (If not, we could hang the author for using language that deliberately leads us down a false trail.)

By the way, I read this book a year ago and recognized the excerpt. Great story–or I should say stories.

The perfect tenses (past or present) imply some completed action occurred before some other event and has some relevance to it.

"to go" in general implies motion or a process; thus in the perfect tenses it implies a completed action with continuing relevance. The continuing relevance can in some cases imply the subject has not returned

But not always:

I have gone to England every summer for the past ten years

The modifiers "every summer" and "for the past ten years" rule out the possibility that the subject has not returned (you can't go somewhere you already are).

I tried to change "gone" to "been" in all these sentences and it just doesn't seem right.

Been to actually works in those sentences but gone to seems more natural. Using "been" also seems to shift the meaning slightly in someways.

"had gone to law school" for instance seems to imply completion more than "had been to law school" would.

Is this use really common?

I think your concept of contrasting gone to with been to is too strict. Yes, been to implies somewhere you are no longer (because perfects represent a completed action), but gone to doesn't always mean you are no longer there. It can depending on the context.