Through emailing with Jordi, I realized I should be scraping through my registry to solve my issue of missing logs, etc. I managed to find an entry in:
HKEY_LOCAL_MACHINE\\SOFTWARE\\Microsoft\\Windows\\ CurrentVersion\\Installer\\UserData\\ S-1-5-18\\Components\\A0F466C0F4982CBEB27AF55227F979C6
The Data column for this entry was: C:\\ProgramData\\Notorious Games\\Xsyon\\
Apparently I don't look at my C:\\ directory very often, because boom, there it was, grayed out because it's a hidden folder. So anyone with hidden files and folders will need to enable that setting, or enter the path above into the location bar.
Anyway, hope that helps!