I did finally figure out how I'm going to make Ship Morale have some meaning in the game. I don't want to take away someone's ship just because morale has finally hit rock bottom, but as the ship's morale heads downwards it will affect the crew's efficiency so tasks will take longer. It will probably be in brackets instead of just using the morale as a percentage multiplier. So once the (1 - 100) morale goes below say, 75, things will start taking longer. Maybe a 10% slow down at that point. Once it hits zero you can probably look at things taking double the normal amount of time.
Morale will still have a major effect on combat, and you probably don't want to try Jumping to a new star system with a ship whose morale is in the gutter. It's not good to be sloppy when entering jump space.
Granting Shore Leave at a colony or space station will improve morale tremendously on a ship, although it will be a 12 hour or so action and cost the ship money, most of which will go to the colony owner, depending on the level of the Entertainment district at the colony. Just letting the crew blow off some steam at a mining outpost with no Entertainment district will help some, but some of the larger colonies will have higher level amenities that will top that morale quickly.