Possible solution: use bitcoin cryptography to identify assets and shareholders, store all the data off-the-chain.
I developed a JS demo. It doesn't store anything and doesn't require any server-side software. It just allows to create share transfers and to process the list of such transfers (sources and sample data here).
1. Shareholders create share transfers via requests of the form:
Quote
{datetime} SEND {amount} OF {asset} TO {recipient} {sender's signature}
Sender is identified by signature. If sender is the asset, then it is share creation. If recipient is the asset, then it is share destruction.
2. The issuer appends (either manually or automatically) such requests to the list of transfers, then processes it and creates the updated list of shareholders.
This solution is not very scalable since it checks the signature for each transfer and it may take much time. I have some ideas how to improve it, but it might make things a bit more complicated.
Do you think this approach/tool is useful? Maybe the original problem is non-existant or already solved. Maybe the easiest thing is just to have a spreadsheet or some file at pastebin. Maybe we should develop an assetcoin, use colored coins or ripple to issue shares. Please share your thoughts before I put any more effort into it. Thanks!