Editable stroke profiles
Add a robust window where you can non-destructively edit the stroke profile (maybe with Bezier handles). This would allow users to taper strokes beyond the good but limited presets in real time.
Ben, using Width Tool you can edit width of strokes, inserting special markers in places where you need them to be wider/narrower, symmetrical or asymmetrical.
Perhaps you know about this already. If you do, but it does not solve you problem — please comment back.