I agree that ideally one would somehow get that data automatically as well (it's just that writing the scripts for automatically submitting is much easier than writing scripts for automatically retrieving...) I've already emailed the two OriginStamp devs asking for thoughts on how users could automatically get the list of hashes for each day that concerns them.
There's some email functionality in OriginStamp which might be reusable for this purpose, in which case one could include one's email address in the shell script and get one email a day listing the hashes you made and containing an attachment with that day's total hashes (so you can verify that your hashes are in the master list, that the master list hashes to the master hash, and then look up whether that master hash's corresponding Bitcoin address has received a transaction or not that day).
1) No reliance on external archives, so all the data required to prove a timestamp should be automatically downloaded after the stamp has hit the blockchain. This should certainly include the necessary subset of the "OriginStamp archives". I'm not sure if it needs to include the blockchain or not.
2) Automatic verification that my requested timestamps have hit the blockchain on schedule and the data required to prove the timestamp downloaded and saved.
Both of these could be done in client software - I have no objection to the principle of the system which seems sound to me.