Is there a similar keyboard toggle for limit the selection to visible?
Yeah, I couldn't find any reference to that anywhere, but yes, would be useful. I am learning so much here.
I have a custom shortcut for this using the Q key. I created it by putting the data below in User Preferences → Input tab → 3D View category → Mesh. When adding the shortcut, the Context Attributes field may appear greyed out, but the text inside can be written regardless.
That is great, I love it. Thanks so much. It took me a bit, as usual with blender, to figure out exactly what I was doing, but it is working now.