It seems the game limits the amount of VRAM used for texture streaming to 500 MB by default. To change this, open the config file found in:

%USERPROFILE%\Documents\My Games\The Vanishing of Ethan Carter\AstronautsGame\Config\AstronautsEngine.ini

Underneath [TextureStreaming], look for a line labeled "Poolsize=__" (mine was at 500 by default), and change to the amount of VRAM your GPU has. I'm not sure how this would work for those on integrated GPU's (although I can't imagine this game is even playable on such systems). Also, consider backing up your file before attempting in case things go awry for some reason (it's just best practice, really). Hope this helps.

I have a 780 Ti (3 GB) and used 3072 (e.g. 3072 MB = 3 GB), perhaps you should move yours up to 4 GB or 3.5 GB. For me, it didn't get eliminated but it did seem to reduce it. Hope it works out!

A few more things to try out:

bUseBackgroundLevelStreaming=True --> False
bSmoothFrameRate=False --> True (beware: there are two entries, one under [UnrealEd.EditorEngine])
MaxSmoothedFrameRate=62 --> whatever your monitor frame rate is, e.g. 60 Hz

Note that there are two files, one inside the documents Folder like the OP stated, one inside the game folder called BaseEngine.ini. I made changes inside both files, just to make sure.

In-game I changed the graphices setting from "Fullscreen" to "Fullscreen windowed".

With these changes I could reduce, not elimintate the stutter.

Other tips I have read which might help that I did not try out:
In-game go to options -> controls and set "reduce camera smoothing" to zero.
You could also try to widen field of view.