The game very stubbornly rejects any attempts to run it in windowed mode, and OBS straight up fails to capture it. How does one record themselves running this game?

If all else fails, is it allowed to record this game without an on-screen timer? Fraps DOES record it...

I ended up answering my own question, at least in regards to running it in a window.

First you need to add a file "wme.ini" to the game's installation folder, containing the following:

[Debug]
AllowWindowed=1

Then, you have to open Regedit, go to HKEY_CURRENT_User\LIMBO of the LOST\Video, and change Windowed to 1.