I used to regularly hunt pheasants; they are a challenging bird. Using 51 point AF would probably be the first mistake, if you were trying to photograph birds that were flushed by dogs, or birds that were being shot on the rise, or on the wing. I have not seen a single one of your images, but my guess is that you had LOADS of images where the background was sharp, the things BEHIND the desired focus point were what came out sharply focused.
Did you know the KIND of photograph you were trying to make? Did you have the framing pre-decided upon? I cannot imagine you had too much trouble with the dog or dogs, or shots of the hunters. Like almost any well-understood sport, there are classical ways to photograph it. Not sure how much of a pheasant hunting person you are, so please don't take anything I say the wrong way.
I have hunted pheasants with a 12-gauge side-by-side in both berry brambles, and in open Oregon country, where the shots are typically at 30 to 40 yards. Modified barrel, 1 1/4 oz of #6 shot for the first bird that rises, and for the second rooster, the full choke barrel at about 40 yards with a heavier charge of #4 shot or late season even a 1.5 ounce short magnum load of #4 hardened copper-plated shot...this is for open-field hunting-- wheat stubble, open corn stubble hunting here,not much brush behind for acres and acres. If there was a lot of brush and trees and such behind the birds, AF is going to be tricky. In bramble-type shooting, AF is going to be a nightmare with a 70-200, and the ranges could easily be very short, like 15 to 25 yards, and you need a semi-wide angle lens.
Almost every open-field shot here is at 25-40 yards. Did you try pre-focusing by hand to an approximate range for the rise? Anyway...51 point AF is too many points in many situations, gives too much potential target acquisition priority to undesired stuff, like background brush, limbs, brambles, etc. A rooster himself is a smallish target: if a smaller focus group, like 21 point had been selected, and the focus distance at least estimated and pre-positioned, and a sort of-high-up AF area group had been selected, with the camera in a TALL orientation, you might have had some luck shooting birds that were on the rise, and maybe even gotten a feathers-flying shot or two.
I dunno...I've seen a lot of nice pheasant hunting images over the last three decades; MANY were shot with a moderate lens, like a 35mm or 50mm angle of view. The classic, from-behind-the-hunter-with-rooster-on-the-rise shot with the hunter with the gun up and acquiring the bird is a classic shot, and it's based on the photographer pre-focusing on the DOG, or in being able in typical Oregon country, to KNOW where the birds are crouched, and pre-focusing on that cover, at a rather longer distance, so there is PLENTY of depth of field, and you have actually a 20-foot margin of error. Did you have communication with your hunter? Were they hunting with dogs? Have you hunted pheasant before?
Again, it's hard to know much about how your photos came out or why there were not up to expectations, but frankly, the MAJORITY of the absolute best pheasant hunt photos I have seen were taken well before autofocus was invented, and were shot with shorter lenses, and then cropped. Pre-focused at the right, general distance, like...5 feet in front of the dog, at a moderate aperture of about f/4.5 or so. The easiest focus is pre-focus. A tele like a 70-200 is going to be a very narrow-angle lens. THe issue is that, on the rise, you have about 1.5 seconds before the hunter acquires and takes his top of the rise shot, then the bird's going to move into flight. You then have about 2.5 more seconds. This is being generous. The old-fashioned, pre-autofocus method is the approach you might want to take, with a pre-focus set at the distance the dog is working, at f/4.5, f/4.8, f/5.6 and today, NOT, I repeat NOT in Shutter Priority, but instead in AUTO ISO mode, so you can keep the 1/800 or 1/1000 second shutter speed you'll want.
Again...not sure where you hunted at, or if you know the general behavior of pheasant either hunted dog-less or with dog, but if you have a dog, you have a focus distance to start with.
