I think one of the main assumptions I’ve always had about Traveller PCs is comradery.
Using only LBBs 1-3 each generated PC worked in violent situations, might well have known each other (either in the same service, or in some operation involving several branches), or knows someone who knows someone. They have skills. And, most importantly, they have each decided to head off into a subsector beyond the reaches beyond the touch of the civilized sphere of space, beyond the touch of the very government they worked for. Going back home and settling down isn’t for them. They’ve got a spark of the wanderlust, of a desire to make more of themselves, of not fitting in where you just sit around with a job.
In my assumptions about the setup of a Traveller game, the PCs spot these qualities on each other. They sniff them out. They know, “You’re one of us.”
In my assumptions every PC in a Traveller game trusts the other PCs. In one way or another they’ve proven themselves, they are dependable in a fight, you know they’ll have your back. I’m not saying one has to play this way. I am saying I think the game works really well when the group starts off this way.
I also think, extending form this line of thought, if there is a ship, the ship is everyone’s ship. If a PC dies and a new crew member comes on board, some fictional background details are created to make him a brother or sister of arms, trusted and loyal if not to a cause then to fellow soldiers, and he or she is made a member of the crew and invested in the ship as well.
If everyone is not invested in the ship, then all sorts of confusion about risk assessment, investment of time, what missions to take or not take, get all confused–because the priorities of a guy just trying to make some Credits vs. a guy trying to float a starship’s payments are just so different. (Which I think is the problem you ran into.)
Having everyone have equal equity in the ship (just by declaring it so) means the group is more cohesive. And the ship is a focus for the everyone’s attention. They want it in working order, they want it repaired, they want it safe, they want to all hurt the summabitch that did it harm.
I truly think a Traveller campaign works best with the PCs as friends–bound by the very qualities that sent them looking for adventure beyond the reach of civilization and bonded by the fact that space travel is dangerous and surviving in this part of space is hard… and having someone you can trust to help you survive is a really, really good idea.