After a number of failed experiments, and watching a few videos by Scott Manley (hallowed be his name), I came up with the Space Cheetah 1: a much more efficient rocket, more than capable of landing on the Mun and returning to Kerbin.
Having to land near Jebediah’s stranded lander did make things a little trickier, but I managed to touch down within 14km, and Jedediah covered the distance with his jet pack. And so the two brave heroes boarded the rocket for the journey home, blissfully unaware of its lethal design flaw.