Many, maybe even most, suicidial people do not think about all of that. It's why some throw themselves in front of a train or jump off a building in daylight despite this causing severe trauma to bystanders.

They are in an acute crisis and for the most part cannot think of anything but ending their life. Whoever will find their corpse is often not a concern whatsoever.

We can control for location of the hanging. We just need a little more data.

How many hangings in the US over the same time period as the "seven" mentioned above in similar locations: in public, from trees.

I'd bet that those seven are disproportionately represented in that data set.