It's very close. The only thing off is "considered" which seems out of place -- I would use a verb that means more or less "to say" to keep in line with the idea of reported speech.

Amos Root said he was surprised to see the broad claim made that the Sci. Am. was the first publication to announce that the Wright flying-machine was a success. He pointed out that Gleanings had announced it to the world a long while before the Scientific American had taken any notice of this wonderful invention.

Also the ellipses in the second quote are not necessary. You only use these for direct quotes.

The had ... had structure you question seems fine to me. It makes perfect sense -- Gleanings did something before Scientific American did something before something else happened. Although it's acceptable to change it to the simple past:

"before the Scientific American took any notice of ..."

But this does not replicate the structure of the original, direct quote.

The attempt at conversion in the question looks to me to be a proper rendering. As Andrew points out, "considered" is probably not the most idiomatic word choice.

The second part of the question appears to ask why

Gleanings announced it to the world a long while before the Scientific American had taken any notice of this wonderful invention.

was chosen in the source text instead of

Gleanings had announced it to the world a long while before the Scientific American took any notice of this wonderful invention.

Indeed, the second option seems to make better use of the past perfect than the text.

However, the text is not necessarily wrong, the way

Gleanings has announced it to the world a long while before the Scientific American had taken any notice of this wonderful invention.

would be.

The third example is wrong because the present perfect (has announced) is strictly more recent than the past perfect (had taken). However, the simple past (announced) is not necessarily more recent than the past perfect, even though the past perfect is usually used to convey that something happened further in the past. In this case, the word "before" conveys enough clarity to the ordering of the events. The usage in the text is not wrong, but the fact that this question was asked shows why it's not ideal.

Typically we mark reported speech with a backshift of tense. For example, "Root said he had been surprised..."

Here, however, there is a nesting of reported speech (you reporting that Root had been surprised by what Sci. Am. had claimed) together with a sequence of events in the past. Using the past perfect and the simple past to keep that sequence clear would be good. But there's far too much going on to worry about the nuances of marking reported speech. You just need to aim for clarity:

Root had been surprised at the Scientific American's broad claim that it was the first to call the Wright flying machine a success, since Gleanings had announced this wonderful invention to the world long before S.A. had taken any notice of it.