Will a new D800/600/D4 improve my work?

The D800 has improved my work. Note that I stepped up from the D200, a greater step-up than you are pondering. The D800 has improved my work because it has challenged me to be a better photographer. Wanting to get the most out of this camera, I am having to re-evaluate my techniques (hand-holding, using a tripod more, better exposure technique to exploit  the greater DR of the camera, post-processing, etc.) as well as my lenses. I don't mean this to sound daunting; I'm having a blast, and I think my work has improved with this camera. Not sure I'd trade up from a newish D700 like yours, but from a DX camera I think the decision is a no-brainer. Good luck.