>>4312473That shot in particular looks like your hands were shaky. Even at speeds of 1/1250+, if you're shooting 600mm and your technique is shit, it's gonna be blurry. Stopping down can help if it's a lens issue, but you can figure that out for your particular lens by setting it up on a rock solid mount and taking test shots at different F values. My Sigma 150-600 F6.3 doesn't seem to have that issue, but each one is different, of course.
As for technique, you have three points of contact with a telephoto lens- Your hand on the camera body, your hand on the lens, and your eye at the viewfinder. You want to place your lens hand as far out as possible to maximize stability, while using that hand to shove the viewfinder as hard into your eyebrow as is reasonable. If you're getting low to the ground to meet your subject, tuck your elbows into your body and make your legs an immobile platform for your torso. We both use a Canon 80D which has a 7fps burst shutter. I feel comfortable shooting as slow as 1/250s on a still subject, because I'm burst shuttering a bunch of shots; at least one of them will be nicely sharp. Your mileage may vary etc.
