Looking for a properly bleak game for a paper.

[Lord Shark]

Polaris (the one by Ben Lehman, not the French submarine game).

 

[Haiku Elvis]

I'll third 10 candles.
Here's a podcast that breaks it down some
Dice exploder - 10 candles
Also Trophy Dark although unlike 10 candles it is possible for your character to survive.

 

[Gorgon Zee]

It's a bit old now, but maybe Grey Ranks Grey Ranks (role-playing game) - Wikipedia

This. All the way. It's GRAVE OF THE FIREFLIES levels of sad.