and you're not willing to compromise on ISO sensitivity to achieve it, make no bones about it: The Nikon D810 is the camera for you. Like the D800 before it, the Nikon D810 is a clear Dave's Pick!
In terms of the Nikon ... The D810's AF shutter lag measured 0.212 second using single-area (center) AF mode, 0.235 second with flash enabled, and 51-point Auto Area AF lag measured 0.302 second.