Hello,
Sorry to hear you are having trouble.
I would like to start with having you delete your settings.ini from:
\Documents\My Games\Star Control
After, skip using the Galaxy Client and try running StarControl_DX11.exe from the current install directory directly (again, with the Galaxy Client closed). It should be in:
\Star Control - Origins\Game
with a bunch of its other files (don't mind that my screenshots are in Steam, you should still have the same files for the game):

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If that still fails, to a cloud drive (Google Drive, OneDrive, PasteBin, DropBox), please post your RunLog.txt from:
\Documents\My Games\Star Control
and post a link to it here in a reply. I would also like to know if a new settings.ini was created after the direct run attempt.
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Sean Drohan
Stardock Customer Service Manager