When watching, I first assumed that it was set around 3300, 1000 years into the series' future. However, that doesn't sound right, given what happens at the end of season 2 and the very specific number of years mentioned. Did I miss the exact date?
No, you did not. All that's mentioned was that the ship was left by the crew about a thousand years previously. Up until the end of Season 2, it was assumed that it was about 1000 years from the shows "present", which, of course, is now a subject of uncertainty.