I don't mean to be harsh here, but clearly, you need some training on what you are doing. The 1/200 vs 1/250 has ZERO to do with you getting motion blur shooting strobed work. When shooting strobes that are overpowering ambient the light from the STROBE is freezing motion, not the shutter speed. Your results would have been EXACTLY the same had you shot at 1/60 of a second. This is a fundamental tenet of shooting strobed work.
Second, you're shooting Alien Bees. ALL strobes have a flash duration. The more powerful the strobe, and the more of it's power you are using, the longer that flash duration. And long flash durations lead to blur. In your case the blur is not from the strobe, at least not primarily, it's from you moving the camera.
The 1/xxx rule comes from the old days of film and don't apply to the world of high-res digital. We are LONG since past that. And that rule only applies in daylight anyway.
So here are your possible solutions:
1. Put your camera on a tripod 2. Get a lens with VR if you plan to keep shooting at 1/xxx without a tripod 3. Get strobes with faster durations, or wind those 1600s back a stop 4. Trigger the strobes with PocketWizard Flex units which will let you shoot shutter speeds to about 1/1600 or so without issues.
Again, the flash sync speed had absolutely nothing to do with your results here. And if you are lamenting the D600's 1/200, try looking at the Canon cameras in the same price range. They are 1/160 or 1/180.