After two weeks of battling with my receiver setup, I finally found the problem: The output stage of my home-brewed GPS-disciplined 10MHz reference was clipping on one side, which caused the AOR AR5000 to misbehave. My reception cleaned up as soon as I connected the rubidium reference instead of the GPS-locked source.
The feed is not optimized because I’m receiving only 8dB of Sun noise above cold sky, but this was nevertheless good enough to receive and clearly copy by ear the ON0EME beacon bouncing off the Moon.
Next: Optimize the feed and connect the power amplifier to start transmitting my own signals towards the Moon.