Is it viable, by any stretch, for a group of adventurers to turn enough profit to maintain a large (1800-ton) ship?
Yes, assuming they're not doing pure, boring commerce. The referee can throw them all sorts of fun jobs like
* custom (dangerous) delivery services ("take these smoking crates of smallcraft-sized antimatter bombs and discard them at this reclamation site waaaay over in this sector...")
Professor Farnsworth said:
"Good news, everyone. Tomorrow you'll be making a delivery to Ebola 9, the virus planet."
"Good news, everyone! Today you'll be delivering a crate of subpoenas to Sicily 8, the Mob Planet!"
"Good news everyone. You'll be delivering pain medicine to the hive mind of Nigel 7."
"Good news, anyone. The Swedish robot from Pi-kea is here with the super collider I ordered."
"You heard the good news everyone! Save the Earth, et cetera et cetera! Bye!"
"Good news everyone, I'm still technically alive! Yes! But I need to you to dispose of this crazy ass experiment that almost killed me. You'll have to throw it into the sun itself, for only the thermonuclear inferno of the sun has enough energy to ensure its total destruction!"
"Good news everyone! That's what the Professor would say if he weren't in jail facing a life sentence."
* the usual-extraordinary, "I'm getting too old for this sort of thing" mercenary-altruist ops:
Leia said:
Help me, Obi-Wan Kenobi; you're my only hope.
(and yes, Death Stars are permissible in a referee's game if that's what the players want.)
Cornelius said:
The guardians... gave the stones... to someone they could trust... who-who took another route... she's supposed to contact this person... in a hotel... and she's looking for the address. Easy.
* (dangerous and/or fascinating) scavenging jobs:
Firefly said:
"Illegal salvage." The captain says. "Lowlife vultures picking the flesh off the dead."
"Should we deploy gunships and bring her in?"
"Do it."
Itself Surprised said:
"You let me sleep while you chased that junk down, matched orbits, grappled it? You realize how much time that wasted?"
"You needed the rest," the small, dark man named Dorphy replied, looking away.
...
"I've got a feeling it's alien," he said.
He entered the small open area before him. Then he had to duck his head and proceed on his hands and knees. He began to touch things—fittings, switches, connectors, small units of unknown potential. Almost everything seemed designed to swivel, rotate, move along tracks. Finally, he lay flat and crawled forward.
"I believe that a number of these units are weapons," he called out, after some time.
He reached the big housing. A panel slid partway open as he passed his fingertips along its surface. He pressed harder and it opened farther.
"Damn you!" he said then, as the unit began to tick softly.
"What's wrong?" Dorphy called to him.
"You!" he said, beginning to back away. "And your partner! You're wrong!"
He turned as soon as he could and made his way back through the lock.
"Ditch it!" he said. "Now!"
(Roger Zelazny)
* exploration jobs ("go and find out if those super-high-tech aliens in that remote sector want to trade or want to burn you to a cinder")
* bug hunts:
Aliens said:
They mostly come out at night, mostly.
* repo men (Crime boss Big Daddy "Starkiller" Gaaruudin skipped. Go find his yacht and bring it back to our yards. What could go wrong?)
* running a freighter "escort service" -- and by that, I mean they escort small convoys of traders and freighters, protecting them against pirates and tradewar and aliens and Shivva-class patrol cruisers and...
My favorite: all of the above, under an "Odd Jobs" category.
I would suggest that their actual duties and purpose fall in line with the players themselves. What do they like to do? Based on that, customize a situation that scratches their various itches, with a generous dollop of plot complications and difficult paths to achieving their own goals.
And if they're casual on the whole thing, then give them whatever is going to be the most fun for everyone, via a Patron.