Just a thought,
Using the footage already provided. Using After Effects or equivalent, remove camera shake (or at least minimize it). You can add it back in during post.
Render the footage for use in compositing.
Use a stylize/find edges filter to outline the edges of the existing geometry such as the doors.
Using that filter you should even be able to get a clean track off of the floor as it outlines the floor tiles.
Render the footage for tracking.
I use Icarus to motion track (it was free and I have had it a long time) and the camera shake would likely be my undoing which is why I would probably take it out in order to track. I am going to try it both ways and see if I can get a clean track even with the shake. I am confident I can get it with the Find Edges filter.
Wade
P.S. Yes this is my first post