Find another locksmith! The only thing holding the broken key part in place is the spring tension on the lock's leaves. A good locksmith will fashion two shims that can placed on either side of the key's cut-aways. That will allow the leaves to be lifted (fully depressed) and relieve the leaf spring tension on the key's cut-aways. The shim needs to be full height and length with a ramp on their front end and of thin enough material to fit between the key and the lock cylinder opening.

If someone had a Dremel tool and a set of feeler gauges they could probably make them. figure out that thickest shim you can get into the space and then use an abrasive wheel to cut the shim into the proper shape, leave as much of the original shim material to form something of a handle so that you can manipulate the modified portion of the shims into place alongside the key part.

The broken key part should be pretty easy to remove with no tension holding it in place.