Are you trying to lock down the shot OR smooth out the small vibrations?
For smooth - You probably only need to track transformations (not rotate or scale, etc) The shape on the left might not be necessary. Before using stabilize, make sure your Surface (blue rectangle) is locked on the track region. If it drifts you may need to find a better area to track. If solid, go to stabilize module and smooth only x,y and rotation. You can also increase/decrease the smooth.
You can also use stabilize module OR Mocha track exports to lock down the motion. You may find some tutorials useful for this.
Lastly… there is an interesting workflow for inverse stabilization (stabilize precomp) to lock down shot based on Mocha tracking, do your comp, then reapply the motion. This can be achieved with the MochaImport+ script for AE and Nuke OR with Mocha data on its own. Maybe worth exploring, but for pull back camera motion, not as common.
Hope this helps! Looks like interesting footage, please share when you are done.