I think that you actually mean that you were using a smaller aperture because you were using a wildly inaccurate focusing technique?
Prefocusing on fences is one thing (although I tend to avoid it wherever possible unless blind-sighted) but prefocusing on a random point on the ground is a touch bizarre.
There are many reasons for using a narrow aperture, but poor focusing technique isn't one of them. Your best bet would be to track.
As Twizzel and corny have said, a 70-200/2.8 is pretty much the base level lens for equestrian photography, especially from an event photography point of view.
For editorial, I'll use anything from 15mm to 500mm.
The reason why the 70-200 would be better that your 70-300 is purely down to the max aperture of your lens. Wider aperture means that AF is faster and more accurate. Quality has nothing to do with it.
As for stopping down, the narrowest aperture that I'd use for EQ work would be f/8 but that would be with a clear background and wanting to pull the sky in. Otherwise I'm at f/4-f/5.6.
F/16 is far too tight.
As for the set of photographs, having looked on Flickr, I'm afraid to say that I'm not that impressed.
There is very little selection in the set and it appears that you have uploaded every single frame in each sequence without regard to timing or conformation of the horse.
There are several frames that need straightening and the framing needs much more attention to detail in that you have cropped random body parts
(noses, hooves, tails etc) and missed the ground line on several shots where it would have been better left in.
You need to show the horses in one of three positions (according to taste & use): on the rise to a fence having taken off, breasting the fence, on the descent before landing.
Pictures of the approach and departure are rarely used and to be honest normally show the animal poorly, unless on the first stride of a recover to gallop on an XC course.
As for flat work, configuration of the stride is everything.
Out of your set of 123, I'd say that only 23 were really worth showing and that number would probably halve to avoid showing more than one shot of a combination at a fence.
Of those however, most are crippled by too narrow a DoF (as mentioned above) and some frankly quite weird processing with too higher black level and too much contrast.
The above is all based on your claim to be an ex-professional photographer btw, because there are errors in there that should never have seen the light of day (wonky shots, amputations etc).
