That's an interesting relationship with Enterprise - I've yet to really watch that series.
Star Trek's been a family thing for me as well; my mom is a fan - she watched VOY:"Endgame" during its premiere 4 days after she got married. Star Trek was always playing in the house, so me and my siblings gravitated towards it.
Lower Decks was probably 2/3rds of my coping strategy for the death of my grandmother.
Zhush/zhoosh could work - I don't think the word is commonly used enough that it would get confusing.