How did Gildor's messages get to Aragorn and Rivendell so fast?

[Inziladun]

Originally Posted by Ivriniel

The question for me is whether or not there was a residual capacity of the Three. Galadriel's commentary in Lothlorien about the Rings, or other comments I read, implied that the Rings would not become entirely worthless, but merely overly impotent to do anything great.

Are you referencing this quote?

'If you fail, then we are laid bare to the Enemy. Yet if you succeed, then our power is diminished, and Lothlórien will fade, and the tides of time will sweep it away.'

She says our "power is diminished", making no mention of the Three. With the destruction of the One, the Elves are shorn of that power given by the their Rings. Notably, after refusing Frodo's offer of the One, Galadriel says:

'I pass the test. I will diminish, and go into the West, and remain Galadriel'.

I see no reason why the Three would not instantly lose their virtue when the One is gone. The Nazgûl instantly fall at that time, intimately tied to their Nine Rings. and though we don't see the start of it, Bilbo's age catches up with him incredibly quickly after the One is destroyed.