Stabilizing the inverse transform of a system
Like you mentionned, you cannot cancel a right-half-plane zero (or a zero outside the unit circle) by placing a pole on it. A unstable pole in your compensator will make the command of your controller unbounded (i.e. it will reach infinity). 

There are no ways to cancel a right-half-plane zero. It's sometimes possible to "remove" a right-half-plane zero by chansing a sensor position.

From Murray's book http://www.cds.caltech.edu/~murray/books/AM08/pdf/fbs-limits_18Aug2019.pdf


  The existence of the right half-plane zero can be removed if we choose to measure
  the location of the vehicle by the position of the center of the rear wheels instead
  of the center of mass. 


Edit : A right-half plane zero can also be caused by a time delay. Delays to computation can be reduced, but some other delays cannot be avoided.

Edit 2 : I will try to answer your other questions later.