Meh, just wait for the first private flight and ask them to send up a few panels to construct the 1:4:9 monolith, they'll probably do it for "free", they'll be geeks too after all, and probably just as soon as any effort to do this in any other way could work.
The lazy programmer way would be to recognize there's already one up there, it's just been deliberately buried. Kickstarter a digging project in the Clavius area.
Is this more about putting a 2001: A Space Odyssey reference on the moon for fun or leaving a record of our civilization in case it destroys itself? I'm in favor of the second, but the first doesn't seem much different from carving the Coca Cola logo.
Now imagine humans do find some artifact somewhere, they develop subtle theories and even religions based on it but in fact that was just an object set there as a prank, funded by alien fans of some alien movie 2001 equivalent.
It can't possibly cost that much to calculate a trajectory and send a giant single-stage rocket, can it? If we remove the monolith erection requirement, I think this gets much cheaper.
I'd guess that the cost is not just in the rocket itself, but rather the team, research, tests/trials, fuel and logistics of the entire operation. Getting to space is one thing, getting to the moon is an entirely different ball game.
My thought is that we can piggyback on Nasa's earlier work on fuels, and since our goal is just to hit a big gravity well (not at a specific point) our mathematical model for trajectory just has to include the earth and the moon.
Lander: "I was supposed to build it eighteen inches high."
Crowd: "This is insane. This isn't a piece of scenery."
Lander: "Look, look, look. This is what I was asked to build. Eighteen inches. Right here, it specified eighteen inches. I was given this napkin, I mean..."