Sending something to the moon is no small feat and there are plenty of ways we could test the concept by putting Bitcoin in other interesting places as an MVP (minimum viable product)
Mariana Trench – we could put a private key to the bottom of the ocean, possibly the Mariana Trench. Same concept except it encourages ocean exploration to recover it
Garbage Patch – we could put a very small private key (or multiple private keys) in the pacific garbage patch to help incentivize ocean cleanup
Bitcoin Balloon – we could put a private key aboard a superpressure high-altitude ballon. Balloons like this can support a small electronics payload and one is currently at 600+ days aloft with 33 non-stop circumnavigations of the earth.
Earth Orbit – we could put a private key in Earth orbit to incentivize a solution to space debris cleanup. This could simply piggyback on any long-term satellite.
Lunar Orbit – we could put a private key in lunar orbit, considerably easier than landing.
Mars – debatably harder than the moon but it might be worth focusing more on Mars, since that's the place where it would be especially impressive to incentivize exploration.