The downloader / installer keeps getting stuck at 97%, with the description "executing setup". After 30 minutes or so, an error message will appear, saying the installation failed. Any ideas on how to proceed?

I've tried with both Galaxy and Galaxy 2.0, deleting and reinstalling the game, and changing the download path.

I had this issue with Alan Wake, it was exactly as described. What I found is that the game was actually installed, it just wasn't removed from the download queue.
Go to your GOG games directory, run the game executable and confirm the installation is working.
What I did next was remove the game from the download queue, then I scanned my file system for games and it appeared in my library as usual.

How did you remove the game from downloads? I tried clicking the x but it didn't do anything?