I have a similar setup, but I use a projector and a standalong open-cockpit. In other words, there's no monitor I can put the TrackIR "eye" on top of.
My solution is:
1. Affix the reflective dot on my headset microphone, which is around my chin.
2. Buy a "ClosetMaid All Purpose Hang Up, Silver #3551." Home depot has them in the "home organization section, but Amazon has them too
here. 3. OK, look at the photo at Amazon. Imagine tipping the thing back, so that the large square end acts as a base, sitting on your tabletop or just behind your keyboard. Attach adhesive rubber feet to the bottom.
4. Using Zip Ties, attach the trackIR "eye" to the top of this rack, facing your headset microphone. You'll find the spacing and height is perfect. It is also extremely stable, and it doesn't vibrate.
The only problem with this is that I don't see any way to mount the vector expansion to my chin, which is what this setup would require - it is to low, relative to your face and head, to use the baseball cap, I think. Experimentation could prove me wrong.
Hope this helps,
Llama