I decided I'd use the Sugru graciously supplied by Instructables and Sugru for a contest to create a new handle for the lid.
Step 1: Create the handle support
I separated a piece long enough to make a ring the size I wanted the handle to be by using a pair of pliers to bend the strap back and forth till it broke. I flattened out the rough edges.
I used a small bottle of appropriate size to bend the strap into a circle without kinks.