The first problem probably depends on Zeta 1's goal prioritization. It never happened when I played the mission, but CT27 experienced a bunch of problems in a different mission where the AI simply wouldn't depart when it had an active goal, regardless of that goal's priority.
Also, it turns out that Zeta 1 was able to accept player orders. If ordered to guard a ship, for example, that would be a higher priority and Zeta 1 would never jump out. I've edited the mission accordingly.
This is unfortunately a more difficult task with the MediaVP model than it was with the retail model. Instead of attacking the subsystem from any angle, which worked in retail, it is now necessary to attack from the side. Attacking head-on will impact the edge in the middle and will not cause damage.
I am uploading another version to fix the Zeta 1 departure issue.