I think the following would be neat to give a more sketch-like appearance.

Implement either a new "arrowhead" type or stroke profile which would allow open curves (or a cusp shared by two line segments) to extend themselves beyond their end-points by a fixed amount or a percentage of the segment length. The extensions would tapper to a small bevel or point.

The effect would be similar to what you often see in architectural renderings where lines forming the corner of a building extend beyond their intersection.