Any tools for doing quaternion stuff?

Not meaning to be smartass-y, but if you have such requirements, you're using the wrong tool in using AE. Al this and more can be had in advanced tracking tools like SynthEyes and I'd think hard whether it's worth spending weeks and months developing complex scripts and expressions that can be done better elsewhere in the first place.

Mylenium

If the track is accurate, you can Create a 3D null, position it at 0,0,0, select all of the 3D layers and the camera and Parent them to the null, then reset the Nulls position. This will put the first 3D solid, text, or null you added at the comp center. Everything will be right side up if you establish an Origin and Ground plane, then add your camera and solid using the same tracking markers.

A very good and free tool to do this is the Normalize Track Script. I use it every time I run Camera Tracker.

Anything you do to modify any one of the values Camera Track generates for AE's camera will foul up the track. You can't add an expression or change any one of them without breaking the tracking. The only improvements you can make are options that improve the accuracy, like Advanced Analysis or setting the camera's angle of view. Before you run Track Camera, you can correct lens distortion if you have the right information, then pre-compose before you run Camera Tracker. I have Lens Correction profiles for my Mavic 3 Cine drone and all of my Cine lenses. I even have them for my iPhone. If I am tracking a drone or wide-angle shot, I always throw in Lens Corrections first. It makes a big difference in the accuracy of the track and the placement of 3D elements. AE's camera has no lens distortion so tracking at the edge of a wide-angle shot is almost always a problem.

I hope these suggestions help.