As a former electronics technician, I've grown to respect Ham radio operators a great deal. Besides the public service they provide in emergencies, they're an innovative bunch. Packet radio, amateur satellites, moon bounce communications, slow scan TV (used a lot on space missions like Viking), and the list goes on. Good people, Hams.

I suppose moon bounce (EME) would be so difficult because the moon is probably a lousy radio reflector. The surface is irregular and covered with dust, not to mention that the curvature would tend to further scatter the radio waves. The reflected signals would be vanishingly small, so you'd need a really high-gain antenna, a good low noise amplifier, and a sensitive receiver to pull even modulated CW out of the background noise. While I've never really looked into it, it wouldn't surprise me if the reflected signal is on the order of -100 dBm, maybe even less. Compared to that, a 50 watt transmitter with a big antenna in orbit around Mars would probably provide a stronger signal.

Here's a link to the proposed AMSAT Mars Communications Satellite. Yours was the first I'd heard of this project. Very cool! I hope they go for it. I'd be willing to donate some money if needed to help make it happen.