Ogul's iddea of them being private sector astronauts is what I had in mind. Reed and Ben would have been the actual astronauts, with Sue and Johnny being their passengers on a private space flight.
I like the idea of sticking to the original conception, but honestly, you'd really have to make it something of a comedy.
I mean, if you read the original comics, it is laughable. Reed Richards tries to convince the US government that they need to do a space mission (to Mars, was it?) to beat the Russians - I mean, "Commies." The government sorta disagrees, I guess, but they also apparently build a spaceship for him anyway - just they won't let him take off until he's done a little research into the safety of space flight, those cowardly bureaucrats! The first thing Ben brings up is the effect cosmic rays would have on them, but then Sue calls him a coward and he breaks a desktop with his fist (was he already super-strong?) and, apparently right then and there, they sneak onto a restricted military space-pad, take off and, just like Ben feared, are hit by high doses of biologically altering cosmic rays.
Really, the first story should've been the entire family on trial for trespassing, theft of government property, child endangerment, public endangerment and millions of dollars in destruction of public property.
It would have to be completely comical.