First I would like to say, you have been posting some exceptional shots. Better than what I can typically produce.
But always looking for improvement is always good. So my comments below are given in that light.
There was a point I wounder the same about Joel's birds... the eyes were just exceptional. Luckily, Joel is very generous in sharing his shooting parameters. So I went through a lot of his posts to get a handle on what's different. You will find his shutter speeds are typically quit high, and he is not afraid to bump his ISO up to get the higher shutter speeds (and exposing to the right helps reduce the noise problem). I never liked high ISO's to get the shutter speed up (unwarranted fear of noise) and did not follow his lead, but out of frustration I finally broke down and tried it... and produced some of the best shots of birds I have ever had and the noise was not that bad. What I learned was shutter speed is key to get the sharpness in the eye, but you still need to get the exposure to the right so it does not go black on you. If you need to bump the ISO up to do so, then so be it. Beyond that, the basics of a good tripod, mount, and a release (don't touch the camera) should help you get good sharpness. I went back to Flickr to see some of your shot settings of a few of your recent posts. You have been running shutter speeds of 1/400 to 1/800 (most of the ones I looked at were 1/400-1/500), and your ISO's were pretty low at 200-400.
I have to admit (and he doesn't even know it), I have learned a lot from Joel and his generous sharing of information. Going through this thread and studying different shots and parameters is one of the best educations you can get. You are past my abilities (I love the clean backgrounds), but I think if you could get your shots up to 1/1000-1/1200 second shutter speeds (1/800 minimum), then the eyes would step up to another level. And it is all about the eyes.
I am probably the last person that should be giving advice in this thread, so take it for what it is worth.
Pat