Admittedly, there are some recommendations on the Tarsnap site (http://www.tarsnap.com/gettingstarted.html):
"5. Keep your key file safe
Store your /root/tarsnap.key somewhere safe. If you lose tarsnap.key, you will not be able to access your archived data. The same encryption which ensures your data security also means that there is no way for anybody (including Tarsnap Backup Inc.) to restore your data without this key. There are many ways to keep it safe: Copy it to a different system. Put it on a USB disk. Give it to a friend. Print it out (it is printable text). Store it in a bank vault. Pick at least one and do it!"
The only other way I can think of to keep the key even safer would be to use Shamir's Secret Sharing to divide the key up and share it among trusted friends and family. (https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing).
Sharing a key involves downloading it from the server, asymetrically encrypting it with the public key of the reciever, and uploading to the server again. It also allowed sharing with groups via intermediate keys decrypt-able by multiple users.
Obviously it's just a PoC - noone should use it for actually important data, and I certainly don't promise that it's actually secure - but it does (more or less) work. As it requires client-side crypto, it's not an ideal candidate for a web-service either (although one could potentially use browser extensions to make that more reasonable).
What about Hashicorp's Vault?