I have no idea if the 6700 rings will fit. I think they will, but I'm not sure. If nothing else, 6600 rings WILL fit and wont look nearly as goofy on a different crank.
Also, putting different rings on won't make it "pedal smoother" unless the old ones are worn out.
If you want to go full Ultegra I'd just wait until you're FSA bottom bracket wears out (shouldn't take long
) and replace the whole mess then with an Ultegra crank.