So here’s what I did:
I made a strap that is 1.5″ wide, and 50″ long, in a loop, with both fusible interfacing and a layer of batting inside for stability. (If you need more direction than that, let me know. Also, if you make one, you’ll probably want to measure how long you need the strap — 50″ won’t be right for everyone.)
Then I got a 99¢ carabiner from Home Depot, and attached it to the strap and the (left-side) triangular split ring that was already on my camera.
The camera hangs down at my right hip, so it’s easy to grab, and it slides along the strap, so you don’t have to worry about the strap getting caught on clothes, or rubbing against your shoulder. Plus, it’s about a million times cuter than the original strap =)