My two cents....take it with a grain of salt, because I'm no expert with long glass.
Spirit looks pretty good, which tells me the equipment is capable of getting the job done.
If the planes were 200 feet away, your DoF is large enough that at least some part of the plane should be in sharp focus. If they are 300 feet away, then the DoF should be plenty adequate. Looking back through some of my old pictures, I frequently shot jets at f/4.0 to f/5.6. so I think you have some room to spare, when it comes to aperture.
I'm leaning towards a very slight camera shake issue. Shooting handheld with long lenses takes some practice and a steady hand. I'm not so great at it, so I compensate by increasing the shutter speed. I haven't shot planes (or anything else, for that matter) in quite a while, but when I did, I liked to keep the shutter speed at 1/1000
or faster. Sure, it can be done with slower shutter speed, but why risk it? For close up action like horse racing, I would try to use 1/2000 or faster. Speed is your friend when trying to shoot action, especially with long lenses.
Of course, the game changes and gets a lot harder when shooting propeller driven planes, and you are trying to get some prop blur. 1/200 or so, seems to be about right, and it takes a talented photographer to pull it off......which is why I don't have any prop plane pictures.