The 1D-III issues have been identified and fixed, and even the "defective" ones autofocus much better than the consumer-grade cameras. The 1D-II models never had any focusing issue, and can be had for quite a reasonable price now. And they autofocus far better than any MF camera system.
BTW, I've used the 8FPS option on my camera on maybe three occasions, and none of them were for actual jobs for clients. With some events, shooting single shot mode will still fill the buffer when shooting RAW if you want to get decent shots of all the riders in the event before it is over. Even if you time your shot perfectly, you're going to want to take more than one of each horse and rider, because the horse or rider may do something to lessen the value of a particular frame.
On a show jumping course, the rider may have the horse jump too soon or be doing something else that they may not want immortalized in an 8x10 in the wall. You'll want to get shots of as many jumps in the course as you can; one shot of the peak moment of each jump. For dressage, the riders are especially fussy; you may not notice if the horse is cantering with the wrong leg leading, but the rider probably will, and those shots probably won't sell. Nor will shots where the rider is making any of many possible mistakes that may not be obvious to the casual observer. In the mass events, you have only a few minutes to get salable images of as many as 25 or 30 riders, and shooting slowly is simply not an option. Even if you don't "machine gun" and your timing is quite good, you are still going to shoot a lot if you want to have a good chance of capturing an image that will sell.
Then there's the issue of focal length; a zoom may not be as good as a prime, but an uncropped zoom shot will handily beat a prime shot that is cropped down to 25% of its original pixel count. My tool of choice when shooting outdoors is the 35-350L; not the sharpest lens by any stretch, but the fact that I can get the framing right in-camera with minimal cropping makes up for it's shortcomings. On the 1D-II it is equivalent to 50-500mm, which is an ideal range for covering dressage and show jumping courses. My second choice is the 70-200/2.8L IS. It has less focal range, but is preferable in low-light conditions. Shooting with a MF back and primes means that you're either going to have to forgo numerous shooting opportunities or else crop many of your images heavily, which kind of defeats the purpose of the MF camera...
A 1D-II isn't that expensive right now, but is far better suited for action shots than any MF system. Image quality is irrelevant for images that you fail to capture because the subject was too far away or the camera buffer is full, or that aren't focused properly because the AF can't track the moving subject accurately enough. And unless you plan to bring a very powerful desktop to process images on-site, the overhead of MF digital is going to slow down your workflow to a crawl which is not what you want when customers are waiting in line. The smaller DSLR files will process much more quickly, and will still be overkill for many of the prints you'll sell.