Dukejazz,
Thanks for that.
I did draft a post saying I'd solved the problem, but I must have forgotten to hit "submit"
For anyone else with the same requirements, here's the procedure that worked for me:
Download Make Faces from here: http://www.smustard.com/script/MakeFaces and install
Explode the drawing twice (like you say)
DON'T group the exploded lines to form shapes (tried that, and it prevented the next step from working)
Use Tools>Make Faces to create faces from the spaces bounded by the lines
Push/pull as usual
So I'm a happy bunny
Steve