Riddling worked fine with what was in effect a heap of earth, but the same procedures just couldn't cut it in the bed. The earth was far more claggy, for one thing. And some areas very compacted. After an hour or so of experimentation with the big and medium riddles, I gave it up in favour of a regime of rake, dig, rake, dig, etc. Weather, work and domesticity permitting, I can get this done in a few weeks.
It's looking better already.