"Photostream is Photostream. You can't split it."
That is incorrect.
You can in fact split Photo Stream events -- but it appears it can only be done from within iPhoto, not Aperture. While not convenient, this is not a problem because Aperture (3.3) and iPhoto (9.3) can open and manipulate the same libraries. (Apple's official documentation is here: http://support.apple.com/kb/HT5043)
If your Aperture and iPhoto apps have separate libraries (as would be expected, unless you've already "unified" them), you can temporarily open your Aperture library in iPhoto, split the Photo Stream events there, then point iPhoto back to its own library.
- Quit Aperture.
- Open iPhoto, and from the File menu, select Switch to Library to open your Aperture library or whichever library contains the Photo Stream Event(s) you wish to split. (See Apple's support pages, which I've linked above, for details on sharing libraries between iPhoto and Aperture.)
- Check your iPhoto preferences' General tab for "Autosplit into Events." Select the setting you want, and close the Preferenes window.
- In the main iPhoto window, with Events selected at the left, select the Photo Stream event (or events) you'd like to split (e.g., "Aug 2012 Photo Stream").
- Finally, from iPhoto's Events menu, select "Autosplit Selected Events."
Quit iPhoto, then reopen the Aperture library from within Aperture. Your newly split events should now appears as (newly split) projects within Aperture.
NOTE: As far as I can tell, there's no "Autosplit" command in Aperture, which is unfortunate. Hence, this cumbersome workaround. If I'm mistaken, I invite the correction, as it'd be far more convenient to be able to do this directly within Aperture. Hopefully Apple will realize (or has realized) this omission and will correct it in a future Aperture update.