Hint: You need a cert defensive and non-combat related ship upgrades, as well as a diverse crew.
For the love of all things FTL, I cannot get full shields AND (what I assume to be the defensive ship system) full cloak... this Zoltan thing is really bugging me... I JUST WANT TO KNOW WHAT HAPPENS AND HOOOOOOWWWW????
... Yet, this is what is making me play even moar FTL than usual. Sooooo I'll keep trying