I to be honest did pre-focus on the feeder. If I could however, humbly disagree with you I will (even though I guess the proof is in the image

). I only say that because I set up the feeder so that it would give me an equal distance or plane from where they fly in and out of on and x axis so to speak. I feel that the bird is well within that "plane" So, not to argue but more to plead my case and maybe make both you and Sparky consider if there may be something else ie. Image Stablization or the like.
I have not done a back focus test and to be honest I am having a hard time recalling whether I have any sharp images. Another project for me to do.
There is absolutely NOTHING wrong with that. Anyone who has shot action shots of any kind has most likely done the same thing at one time or another. I do it a lot shooting races by focusing on a particular point on the track and waiting for the car or motorcycle to get to that point. I also do it with birds when I know it's where they are going to be. I shot a bunch of Hummingbird photos a couple of months ago and did the exact same thing.
The D7000 has enough resolution that you can afford to zoom back in a touch and give yourself a little wider field of view. This gives you a little bit more time to see the bird coming into the field of view, and a bit more depth of field. I have the same lens and same body, and usually shoot birds at ISO 1600 and f/8. The lens works great there and there is hardly any noise. The noise is low enough that I very seldom do any post-processing noise reduction. ISO 3200 should also work quite well with some noise reduction afterwards.
One thing I have noticed about that lens is that it looses a lot of contrast when there isn't a lot of light. Both of your tests appear to have been shot on overcast days and that's part of your loss of contrast. I normally just use my 70-300 when it's overcast because I have come to know that anything shot with my Sigma is going to look washed out and low contrast. Pick a day with bright sunlight, even if your feeders are in the shade, and you'll see a world of difference.
Also, when using a tripod that is locked in place turn image stabilization off. It can induce softness in the image when there is no motion to compensate for.
And finally, waste shots. I normally take bursts of several shots when shooting birds. It costs nothing to take them and throw them away, but many times the first shot isn't as good as another one in the burst, or I find one in the burst where I like the head or wing position better.
Birds are tough to shoot. Keep at it, you're doing fine.