I looked at the gallery files, or some of them. First, I don't see how you could possibly be shooting the equestrian events with the mirror flipped up, or for that matter with a remote. I shoot equestrian and I don't even use a tripod - it's a monopod for me, and I'm using some much heavier glass. I'm more than a little suspicious that those were just hand-held, because I have a pretty fair amount of trouble with "perfect" framing even with a lot of experience. I can't imagine even attempting to shoot sports with the mirror locked up. I can't really even imagine using LiveView - I did that for a few frames yesterday with some slow-moving animals (sheep in pens) and even that was pretty hard.
All of the equestrian shots seem to me to be shot at marginal shutter speeds, usually 1/250th-1/320th, with longer focal lengths. I saw 145mm and 240mm for sure. I can't see your technique, but given the rule of thumb being that shutter speed should be at least 1 / (focal_length + 50%) you're not really there, even if you have good technique. I can see pretty clear signs of camera motion, usually softness in the static parts of the frame - the jumps and their frames, for example, should not be moving at all. I'm guessing that your 55-200 is NOT a VR lens? I know that the Tamron is not unless you just got it in the last month or so. "Strutting its stuff" is shot at 300mm but with a shutter speed of 1/500, which is only just barely sufficient according to the rule of thumb. If your technique for holding it is not excellent, even this speed will be marginal.
Next, you're shooting things in fairly quick motion from relatively close distances. This isn't like an airplane at 2000 yards distance - at 150mm you are no more than 100 feet from these horses and likely closer. Shutter speeds necessary to do this are relatively high. I find that I prefer 1/1000th if I can arrange it, and if necessary that means turning up the ISO. You're not so far from there already, so it should require too much more than base, even on those cloudy days. I have much faster lenses so it's easy for me to get to 1/2000th, and at those speeds it's much easier to deal with both camera and subject motion.
The ones of the runners were shot mostly at around 1/250th, and in all of the ones I looked at (not all), there are clear indications of subject motion. In some cases that's in the extremities - hands, feet - that are moving faster than other parts, and some of it is due to panning or other camera motion.
Finally, the 55-200 is a sharp lens, but some of the older Tamron 70-300's are not especially impressive. Every one of the shots I looked at was shot wide open or very close to that (f/6). Virtually no lens is sharpest wide open (there are a few very expensive exceptions to this rule), and improving the delivered sharpness may require stopping down to f/8 or even f/11 on the Tamron, and even the 55-200 will benefit from f/8 instead of f/5.6. Yes, this is somewhat contradicting the above specification for faster shutter speeds!
There's also something a little weird about the processing in some of these. I can't put my finger on it, but the edges look unusual to me, and I don't think that's helping the impression of sharpness.
Finally, for some of the shots (the hawk and the turkey) are shot at very close to minimum focus distance. I don't know the characteristics of your lens, but I do know that I have a couple of other lenses that simply don't perform as well at minimum focus as they do at a distance. That could well be true in your case as well.
I do agree that all of the shots that I looked at were unsharp, many of them to the point of making the image unusable. A look at these suggests pretty strongly that there are technique and capture errors, possibly combined with lens faults, that are making these images much, much less sharp than what's possible.
_____ Brian... a bicoastal Nikonian and Team Member
My gallery is online. Comments and critique welcomed any time!