So, my noodlings were successful, and I also showed the LA some of the features of her sewing machine. The basic shape for the front of the codpiece is a right-angled triangle, but with the hypoteneuse bulged, or perhaps a rectangle with one corner rounded off. This provides the bulge, when sewn together by the curved edges. I overstitched the edges to prevent fraying, and also to provide myself with a guide for the actual seams. Once I had the front together, I then cut out the back by try-fitting, overstitched its edges, and then made up ribbon loops for attachment via buttons to the breeches. Then I sewed it on most of the way, and left a hole to turn the codpiece right-side-out. Now all I need to do is find a squeaky dog toy, and get some wadding with which to stuff it, and then sew some buttons on to attach it to the breeches.
And in case you were wondering... not that silly. About 3 inches of bulge, and about seven inches high. Certainly less showy than, say, Henry VIII's.