In principle, dating the destruction of Nimloth should be a simple matter. After acceding to Sauron's demands that the tree be cut down and burnt, we're told that King Ar-Pharazôn '...turned then wholly away from the allegiance of his fathers' (Akallabêth in The Silmarillion). That seems to tie in with an entry in the Tale of Years: '3262-3310 Sauron seduces the King and corrupts the Númenóreans'.
On a direct reading, it would be natural to see Ar-Pharazôn's 'turning wholly away' as the completion of Sauron's corruption, so dating the fall of the White Tree at II 3310. However, the Tale of Years confuses this simple picture, because it shows Ar-Pharazôn commencing with the Great Armament immediately after Sauron completes his corruption, and indeed within the same year. In the Akallabêth account, though, there's an evident delay of many years between the burning of the White Tree and the building of the Great Armament.
The combined implication of these sources seems to be that the burning of Nimloth and the complete corruption of the King took place within the period shown in the Tale of Years, not at the end (a date of approximately II 3290 seems to fit the facts). After that Sauron continued to corrupt the Númenórean people in the period to II 3310, at which point Ar-Pharazôn was persuaded to begin the building of his armada.