What kind of super strong bonding agent would be useful to repair a stiletto heel?
If the cobbler told you it was unfixable, it's most likely unfixable. The picture you linked is too small to see much detail, but if you have a question about glue I always recommend This to That as a good place to look up what kind of glue to use.  

But honestly, I don't think any glue is going to hold this in the way you want. The shoes are most likely dead. If they're expensive enough you can look at a home insurance claim, but I doubt that's a route you want to go!