Your timeline sounds correct to me, although when Aragorn sees the eagle from
Amon Hen it is far to the north, possibly reporting to Gandalf. So it is
unclear how often it went back to Gandalf between the 8th and 15th days.
I questioned why the orcs would gain distance BEFORE Aragorn found the brooch
or chose to sleep at
night.
________________________________________
"‘I think he was a silly little man,' said Councillor Tompkins. ‘Worthless, in fact; no use to Society at all.'
"‘Oh, I don't know,' said Atkins, who was nobody of importance, just a schoolmaster. ‘I am not so sure: it depends on what you mean by use .'
"‘No practical or economic use,' said Tompkins. . . .
. . .
"‘It is proving very useful indeed,' said the Second Voice. ‘As a holiday, and a refreshment. It is splendid for convalescence; and not only for that, for many it is the best introduction to the Mountains. It works wonders in some cases. I am sending more and more there. They seldom have to come back.'"