When did Deagol find the Ring?

[Angry Hill Troll]

According to the chronology at the end of ROTK, it was around TA 2500. But in The Silmarillion (in the 1st edition anyway), in the section 'Of the Rings of Power and the Third Age' it says that the Ring was

...found by one of the small fisher-folk that dwelt by the River, ere the Kings failed in Gondor...

In other words, at least 500 years earlier, since the last King went missing in the early 21st century. Which chronology did Tolkien actually intend?