Is it possible for me to save/export a Cubase 6 project in some way that a client can open the project with Cubase SL3 or Cubase Studio 5?
It might work, give it a try. My guess would be CS5 would work but SL3 would not. Of course there might also be issues when opening a Project from Cubase to a lesser version, even within the same version number.
I thought there might be an option to save / export to an earlier version of Cubase (similar to Sibelius, etc.)
Not in that direction - later versions will usually open earlier versions (up to a point - SX3 can open earlier Cubase sessions right back to VST 5/32 and earlier, and then you can re-save the proj and open in current Cubase. Can’t go back very far though.