camerafreak1970 - one thing that I want to make sure is that when you say that you focus and then move, well, you are saying that you focus with a half press and keep that half press down on that shutter when you move, (recompose). I am sure you are but just to dot the i and cross the t I want to put it out there that way.
Now for me I am going to tell you that solid bob has given you great tips and advice. Because your shot was at 1/1000th then I don't think camera shake was a problem unless you was just flat out moving. That bay window does sound like it could be an issue though. I mean you are putting another piece of glass between your lens and the subject. No matter how you shake it out, that extra glass does have an effect on the final shot.
Now I am going to tell you what a wildlife guy that I know tells me. Put that camera on continuous shooting mode with Servo and pop off three or four shots in a row. Now this will not help you when you want to recompose but my wildlife buddy swears that this is the only way that he gets a really sharp focus and he uses some top notch lens. Might be worth a try with your twerps.
