OK, here's my idea
I'm only just figuring out the details, but here are some highlights:
Campaign would last a specific number of sessions. That way, time commitment for new people is limited. I am comfortable asking that everybody commit to four sessions, but not so much for longer-term until they've had a chance to get their feet wet.
My shell of a story idea has two main points:
- Starts within a single solar system.
- Early campaign takes place on one world.
- World is "owned" by ruthless exploiters, who live on the planet's barren (but partially-terraformed) moon.
- People on the planet are being held back from technological growth by "their" government.
- People on the planet are also being artificially dumbed-down by chemical agents continuously released into the atmosphere.
- Some members of the party (~ 1/2) are native to the planet. However, "something" has happened that allowed them to grow in their profession. This applies to professions which the overlords can get away with teaching without losing their serfs to "upward mobility". They need capable slaves, not intelligent ones.
- Some members of the party are non-native, being part of the overlord group, but they've grown a conscience. They're reluctant to let other know, though, because the overlords may have spies watching. So, these people may know part of the mystery, but only mention it as the campaign progresses and they start trusting people.
- Some are not native to the system at all. These are some combination of political prisoners, people who have crash-landed and survived, people who found out too much, etc.
- Starting tech is low (8 or less), but only due to the chemical dumbing-down that has occurred. They actually know how to use some higher-tech devices, but are kept in the dark as to what those devices actually do.
- A major event occurs: the overlords are destroyed when their airless moon-based city's habitation dome is destroyed by an asteroid.
- The destruction of the moon has three effects: Eliminates the bad guys,
eliminates the market for the goods the native population has been producing, and eliminates the chemical contamination that was being continuously fed into the atmosphere.
The idea is that people get introduced to key Traveller concepts during the limited number of sessions. There are also elements of mystery and anger. The characters begin adventuring by joining up with the other characters, and eventually they realize they must unite to survive.
Mustering out benefits are as normal. However, the characters may or may not know about their benefits. Those which their overlords see as a threat were long ago confiscated. Of course, once they're dead, all the characters have to do is get up to the moon and find their goodies (they all miraculously survived -- need a plot device here

). Once the chemicals wear off, they'll even remember owning these things.
Session one introduces the players to their characters (I'm thinking of pre-generating them to save time. If not, session one will include character generation, including various excuses why they don't actually get what they rolled up.

They also learn that the overlords have ears everywhere. They don't really, but they've cultivated that fear to keep a lid on any self-help the natives might come up with.
Session one will also include some unraveling part of the mystery, along with basic survival needs. Some characters will have found pieces of technology over the years, but they don't understand them. They DO realize that theses devices have value, and that value is far less if their masters find out. So, those who have such assets are careful to not advertise that.
In session two, they're given more details that clues them in on how they were being treated. An asteroid crash on the moon occurred between sessions one and two, destroying the moon-base. Changes are beginning to happen on the planet. They're getting smarter, and remembering what they had been taught during CharGen. In some cases they remember what the previously strange devices they have found can be used for.
They'll need to figure out what's going on with their overlords, although without any form of space transportation (yet). They saw the crash between sessions, but won't begin to truly determine the scope of the disaster (for their overlords -- no love loss

).
Session three starts with the population realizing what their overlords have been having them do (i.e. act as slaves producing lots of creature comforts and wealth for their masters). During this session, they party creates a rudimentary ship's boat, and explores the moon. They get all their goodies that they mustered out with (except ships -- if any, those come in session four).
But, they also discover logs on the moon which indicate that there is another host/parasite situation going on aanother planet/moon system that circles the other sun. And, they'll discover that the overlords from that system just recently discovered that their buddies on the party's world are no longer speaking to them. They send a ship to investigate.
The party figure out that the other bad guys are coming, and begin to cobble together a defense system.
The fourth session is the battle between what the party could cobble together on the moon (some formidable armament, actually) vs. the single ship of the other group of overlords. They'll have to deal with them, but they have some heavy advantages: surprise and superior weaponry (it's not exactly a battleship that's coming). After all, the overlords may have more guns, but they're grown quite sloppy, and few people know how to use them. They weren't really expecting a battle.
Once the battle is over, and governments are emplaced on the two worlds, somebody is bound to ask, "What do we do now?".
THAT is what Traveller is all about!
They "steal" one of the few working starships left (actually, their ship elements they mustered out with), grab some of the trade goods they used to make as slaves, and travel to another system ... to "see what's out there."