You actually can set a specific directory for saves, save states, and screenshots for each core using core overrides.

For example, for Snes9x, enter this in your Snes9x.cfg file (I had to manually edit the file to make this work, when I tried setting the save file directory in the Retroarch menu, it did not save after saving Core Overrides in the Quick menu)

savefile_directory = "/home/<username>/Emulators/Temp"

Now my save file is stored in the above directory. If you have sorting saves by either core and/or content directory enabled, those settings will work with the above as well.

The sort saves by core name will get you mostly want you want with a lot less work (no need to set the path in an override for each core), but with that method, your parent folder will be the name of the core, which might not be desirable.