When trying to install games on an ext4 external drive I get a disk write error from steam. Whenever I reset the permissions on the drive to both read and write, not just read, steam immediately reverts that whenever it's opened.
Where is Steam writing to and where is the drive mounted to? If the drive is mounted at /mnt/games, create the folder: /mnt/game/steam, run "chmod /mnt/game/steam" and then have Steam create it's library within there. So in the end, Steam's folder will probably be at /mnt/games/steam/SteamLibrary. This way it shouldn't matter what Steam is setting the permissions to.