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.