Surely if your phone was stolen you also reported this to your local Police station ?
If you did so, then surely someone walking into an Apple store to replace the phone pretending to be you, is additional evidence the Police need to know about. If the Police are interested, they can contact the Apple store in question and obtain the CCTV, so they can try to identify the person concerned.
If the Police are then involved, surely the Apple store will then make a note of this and you will then hopefully get a more positive response from Apple.
This is commonsense to me, but often these days people do not report thefts to Police, on the basis that they won't be interested. If you have not reported to Police, perhaps you should do, to find out whether they can help or not.