It's your lens. Sorry to say.
Turn off your image stabilization..if it has any Nope
Manual focus Had it auto, but it would hunt right past my subject, so I got it close and the let the auto fine tune it (maybe it was wrong, i don't think so though)
Put it on a timer did
Lowest possible ISO 400-800 without flash
Do a mirror lockup as well this is the one thing that I think I can control and than you (both) for suggesting
Set it to Aperture Priority.... so your camera determines the shutter speed. this is how I usually shoot
Let it shoot and do not touch the camera.
Shoot at around F6.3 up to about F10 and see if the image improves. why this range? your reasoning might help me in general
Good luck man.