From Buck's post.

The difference between a ballistic flight (mach 3) and an orbital flight (mach 25) is huge! Maybe as much (in difficulty) as between LEO and a Mars mission (manned).

Maybe the thing to propose isn't so much a landing on the Moon as another kind of trip (with an X Prize contest):

Send a crew of 2 in a week long flight around the Moon and back.
Advantages:
An Ariane V type rocket is sufficient.
The view would be absolutely tremendous!
But the most important thing for the competitive spirit:
The X Prize should crown the first privately financed crew capable of breaking both distance AND speed absolute records!
So it would become a sport event, a media event, a tourism event and a scientific event too.
All this with a much smaller rocket than the Saturn 5.
The trick to break ther record is to launch the capsule at a precise moment, so that when it reaches the other side of the moon in a free-return trajectory, it's also the moment when the Moon is at its apogee (farthest from the Earth).
And the other trick is to save as much fuel as possible so that the capsule can accelerate its way back to Earth.
The distance record would be broken behind Moon Farside and the speed record would be broken just before hitting Earth's atmosphere.
And also, it's a one week event; and 7 days can attract much more media attention than shorter or months long periods.
Because of its particular trajectory shape, this competition could have a name: the "Big Eight". Or "Big 8".

Raoul