Raoul, the mental picture you painted of that trip in the context of a competition immediately made me think of archery. Like archery, the competition is based on skill at aiming, plus strength for distance. A contestant would let fly with a rocket instead of an arrow, and points are scored based on how closely its trajectory conforms to an ideal, say XX kilometers above the Moon at perilune, and how close the vehicle comes in to the designated landing point (hitting the bullseye).

To make it more interesting, not to mention safe for the passengers, you allow midcourse corrections--unlike archery. But the delta V used counts against you, in the same way that strokes count against you in golf.

Which adds up to a sport something like yachting, where skill at seamanship translates into skill at "spacemanship". Tacking against the winds of gravity, threading the needle of the buoys, shaving seconds off your time...

The circumlunar trajectory is only one course, of course. Imagine a Space Regatta, with prizes for most circular Earth orbit, fastest rendezvous, fastest trip to Mars (someday), the Asteroid Belt slalom...it boggles the mind!

Somebody needs to write a sci-fi story about this.