I think you are a bit confused.
Protective Stop is NOT a safety mode. It is a collision error. It is a forced stop. Which is why you can't normally just continue as if nothing happened.
Safeguard Stop and Reduced Mode are what you are referring to as "safety modes".
We ran the same kind of tests with a PILZ representative a while back and every stop has been a shock stop that required us to restart the robot and rerun the sequence, manually.
You can, theoretically, force a signal to enable the robot after a shock but you need a bit more knowledge of programming - scripting - than I know at the moment.
You could, however, just create a small routine that would send the robot back to its initial position. So after you get the shock, you just enable the robot, press stop and then play. In theory you should be able to get a routine running that won't need much from you except 3 button presses.