I have 100 billion STARs available! Who wants some? They are free for the asking.
Here is an idea:
Create a list with all known stars.
Set a few blank fields next to each star. Fields should be "Owner Name" and "LastTransactionID".
Allow anyone to claim a star from the list by updating the "Owner Name" field.
Then send him 1 STAR and update the LastTransactionID for that star.
As a result you'll have a list of stars, their owners, and a transaction linking everything to the blockchain.
There could be issues if one address holds more than 1 STAR as they would merge. Perhaps you could add memo when sending stars, stating which star you've sent. Tracking this might be a nightmare but seems possible (unless someone deliberately merges a lot of stars and splits them again without proper memos).
You could even create a script that parses the blockchain and updates the site with actual information. And if someone merges a few stars -> he gets a blackhole, effectively losing them.