[DonRotolo]

Thanks everyone for your comments. I just got around to actually working on this again (this is the busy time at work), and the very first post (expanded by the second post) was essentially the answer: Sketch a "D"-shaped polygon (or perhaps a box, only the line intersecting the object is important) at the end I want to snip off and use Extrude to eliminate that bit. Repeat for the other side.

The fact that work planes extend to infinity was the key, thanks to MechEng83 (who, I suspect, graduated the same year I did...)

Split, I have learned, is to actually split an object (imagine that!), much like a saw would do, but keep both parts in their same physical relationship to each other, not discarding anything.