So, how long had the Sakamoto's...

and the other researchers been stuck on that island? More to the point, does anyone happen to know precisely when they all landed?

There were various hints provided throughout the course of the game, and obviously I failed to piece it all together... I know killer robots were dispatched 10 years ago, along with Quote who failed his job. Then booster mentions sue not wanting to go but was too young to be left behind, and in her note she mentions the doctor was there to serve their medical needs; the "and did so" part rang unsure, as if she didn't really remember.

At first I was under the impression that they'd arrived few short weeks/months prior to where the game kicks off, but with the gaping 10-year time gap; Arthur being killed by the doctor, and all these other little details popping up here and there, I was starting to wonder.. Has that family been stuck on the island for years?

 

I doubt they were there for literal years, it wouldn't have taken the Doctor years to find the Red Flowers, for Misery to find Sue, etc.

 

You'd think they would have gotten to know the inhabitants and the island better if they were up there for years. I would think that the Doctor, who got his hands on the crown shortly after arriving on the island, would not wait ten years to enact his plan. It didn't seem to take a lot of preparation.