Hi GLM,
I'm a little thick today and am not sure I understand what I'm looking at. Apologies. 

Regarding the sweep path, if you move the drawing tool near another vertex, you'll see a little square appear next to the cursor. This is cue that the line will automatically connect to the vertex and all you need to do after clicking is draw the next points until you finish by hitting the return/enter key. 

From the shapes I'm seeing, it looks like the dynamic extrusion or Gordon tool might work better on this shape though...

Mark