Things only started going to shit for the Rapa Nui people and their monumental culture when (surprise) Dutch colonists showed up in the 1720s
The point wasn't how things
went to hell, the point was this - at the moment someone might have decided "it's time to get going," things had already exacerbated to the point where a viable exit was not an option. Remember, in the moving of a colony, that the very young, the sick (which would have been more than a few), and the elderly or infirm also have to be moved, or else abandoned. It takes a
lot to make an journey as would have to have been undertaken, and they didn't have an infrastructure which would have easily accomodated a move such as to a nearby island.
the infamous tree clearance was either what all agricultural societies have to do (and appears to have been sustainable as any other) or was exacerbated by rats.
Although it is a nice line of thought that there was a "clearance," the fact is that decent trees were scarce at the best of times during the period where some inhabitants would have wanted most desperately to escape. Added to that, the selection of trees available were not weren't all of a useful kind - you can't use some types of wood for much more than nice carvings or for shelter. The types of trees which had wood suitable for boats were fewer than needed, and at least a few would have ended up burned.
You add it all together and it is clear that the constant exploitation of the island and its people - not to mention the complexity of moving an entire culture - made getting out en masse an unviable proposition. That isn't to say that people didn't book for the nearest exit, but the culture was rooted - in both senses of the word.
And the tree thing specifically? The rats, and likely fires from raiders, put paid to any chance of people using the wood for anything useful - simply wasn't enough to build boats large enough. This wasn't deep into the 1800s either, but likely around the mid-1700s . At a guess, things probably went to shit in the 1740s or 50s, as diseases, rats, attacks, and a changing weather system took its toll.