Ask http://www.drivesavers.com if they do such data recovery.

Even I don't go near this issue because in my experience the owner is ready to sue anyone that dares to help. So while I know something it's more about we backup BEFORE we have troubles with a device. Trying to do so later means a lot of bad feelings or worse, flames for anyone that dares to mention this.

What may help but rarely is removing apps you don't need. I've seen that error in low memory situations.

And finally, find a company with the CELLBRITE clone machine and see what it costs to clone that phone.

Again, recovery isn't cheap, fun or something folk have any patience for. Except that link?
Bob