The bad thing, that might be causing your blurriness, is using the zoom to zoom in too much. Better for focus to take the picture in wider frame and crop it on your computer to bring the action in. Even when my horses are all the way across the pasture, I don't zoom more than 2X. Not with that zoom. And because of the delay... take LOTS of pictures and expect to throw out lots of them. It's just too hard to perfectly time something that's running to get the right moment in their stride. You just have to take lots and get lucky. But I took these pics with a Coolpix.
I am impressed. As I suspected, half of the problem is the photographer. :^) I will try your suggestions. Thanks!