Why not propose some kind of X-prize with simple but very challenging goals in space?

The furthest distance ever reached by humans...
This can be done by going towards the moon and turning around it while it's at its apogee. One engine kick could do it from Low Earth Orbit.
The fastest speed ever reached by humans....
For the same trip, because of the longer distance, just before re-entry, the fastest speed will come naturally.
To take a picture of a spacewalker, far enough from the spacecraft so that he'd appear just smaller than the Earth, with the Earth in it and our planet being not larger than 2 degrees to the photographer.

This is a setup of Apollo 8's Earthrise, Mc Candless' spacewalk and farside from Apollo 16 (Earth and Moon are together gibbous):

The goal being to produce this kind of picture with 4 different achievements: 1)further, 2)faster, 3)furthest untethered spacewalk, 4) Earth and astronaut about the same size.

Of course, there would be at least 2 astronauts on that trip.