Everything I have tried, clean installs with IceMage's 2.0.67.2 installer don't do anything, as it keeps just auto-updating before I can even get into options to stop it. I keep having the same "Update Failed" problems when trying to verify files.

2.0.67.2 is the version of the latest full installers, but the current version is 2.0.68.112.

There's no setting to prevent GOG Galaxy from updating. You'd have to rename C:\ProgramData\GOG.com\Galaxy\redists\GalaxyUpdater.exe before launching the application for the first time. Even this might not be enough if an update check has taken place and the update is already queued.