Cycling Routes: Edit start/end points on saved maps?

I've checked the help section and read through reviews, but I don't seem to find any information on this issue. I've created several cycling route maps, but they all start at my house. Now, I'd like to make some of them public... but with more generic start and end points.

When I try to edit a start point in a map I've already created, I can drag the start point icon to a new place and it sits there, but the route doesn't change at all. Even though the market is in a new place, the little blue route line still starts at the original point. Is there any way to move the start point (and end point) so that my routes start/end in a new location?