How does one shoot 9500 shots in a day?....
You've apparently never shot a busy equestrian event. I regularly shoot between 3500 and 4500 a day at dressage shows (more than at other types of horse shows) and I try to keep it to a minimum. (Because I hate sitting at my computer editing shots, so I only shoot single images or very short bursts. I can quick edit/proof about 1200 images a day, via Lightroom, on average.) 10 or 12 or more hours of practically non-stop shooting. I've seen other, less conservative photographers shoot over 10,000 images in a day at those sorts of events . I don't envy them.
OP, my first choice for a backup camera is always the same model, so another 6D in your case. That's easiest to switch back and forth between them, which can be important if using two cameras at the same time. My third camera is a different format, for the advantages that offers.
However, it appears you want the different format and won't necessarily be using both cameras side-by-side. In that case, I'd recommend one or the other of two models: 70D if you want the latest and greatest, especially if you also want to shoot video. Or, a used 60D if you want to save a few bucks.
These two models have control layout and functionality that are most similar to your 6D. They both also use the same memory, batteries & chargers as 6D, so can share those. The AF system of 60D is most similar to your 6D. Now, 60D can't focus in quite as low light and has two fewer AF points, but all nine of the 60D's points are the better "cross type". 70D's 19-point (all cross type) AF is considerably fancier and more complex... for action/sports photography would be a bit better than either 6D or 60D. Also has Dual Pixel focus in Live View, which makes that much more usable. Both have articulated LCD monitors... nice for low or high angle shots. 70D's is a touch screen I believe (and am not necessarily wild about... if I "butt dial" my cell phone, will I "nose set" my camera?).
Depending upon what you shoot, if you get a crop sensor camera you may want one or two crop-specific lenses... but otherwise can share lenses with your 6D. (I have two ultrawide zooms and one compact macro/portrait lens that are crop-only, everything else works on both crop and FF cameras.)