If you don't want to do something smarter, by nature of the file system that Steam rests on, there must necessarily exist some folder s.t. all save locations ex

If you don't want to do something smarter, by nature of the file system that Steam rests on, there must necessarily exist some folder s.t. all save locations exist in a subfolder (recursive) of this folder. You'll use extra space, but you can definitely do that easily. Alternatively, you can keep an environment variable GAME_SAVE_MOUNTS to which you append a -v flag with the desired mount saves. You can that start your container with $GAME_SAVE_MOUNTS and have everything work out of the box.