Singletrack,
Interesting idea, leaving the lock where you're going to lock the bike! Here in Phoenix, people will steal anything at all. My husband and I used to do a lot of geocaching, and I was always amazed that people would steal the caches, essentially small boxes of absolute junk. However, I think your idea would be ideal in a more secure location, such as at work.

I'd been picturing wrapping the cable around and around some place on the bike. But now you have me thinking that with the coils, it probably would work just to wrap it a couple times around the handlebar and let the coils dangle in with the other cables.

OK, thanks again, everybody. Now that I have a few different things to try, I'm motivated to get back to running at the park. It really was a fun workout, because it was so different: short, hard (running and riding some steep hills), and with lots of people around.