As you know, per your question, the preferences in the Preview app only apply to documents when first opened. It seems that OS X has a built in default view for full screen documents. I tried a couple things...
- I opened a PDF to Full Screen and set the view to Continuous to see if this would stick and that view would be chosen next time I went full screen. Not the case.
- I searched every preference file related to Preview (also using 10.9.2) and found no setting even indirectly related to a view setting specifically when in full screen.
I'd say, doing what you want is either not possible at all or at best it'd require getting into a preference setting somewhere you wouldn't want to poke around with. My guess would be it's a setting inside Preview.app's package contents. Fooling around in there can get hairy
As an alternative to setting a new default, the keyboard shortcut to switch to Continuous view is:
So you can just quickly hit that each time you go full screen and the view changes immediately. It's not exactly what you wanted, but it's a very fast alternative.
Hope that helps!