I've found the accuracy of the AF on my 85 f/1.2 to be very good. My workaround for the slow focus is to zone prefocus (using the autofocus) to set the focus in the vicinity of where I anticipate that I will need it.
If I try to focus from four feet to fifteen feet and shoot a frame all in one motion, odds are that I will miss the decisive moment. If I see and anticipate that my next shot is going to be in that range, I will AF on something roughly in that vicinity without firing a frame off. Then, when I need to capture a moment, the lens has to move only a short distance and is very responsive and capable of capturing a shot quickly.