Sorry, but "Untrusted remote storage" and "No server-side processing" are exactly the opposite of what I need.
If the original box is ever compromised, I don't want the attacker to gain any access to the backup. If you use a dumb storage like S3 as your backup server, you need to store your keys on the original box, and anyone who gains control of the original box can destroy your S3 bucket as well. Ditto for any SSH-based backup scheme that requires keys to be stored on the original box. A compromised box could also lie about checksums, silently corrupting your backups.
Backups should be pulled from the backup box, not pushed from the original box. Pushing backups is only acceptable for consumer devices, and even then, only because we don't have a reliable way to pull data from them (due to frequently changing IP addresses, NAT, etc).
The backup box needs to be even more trustworthy than the original box, not the other way around. I'm willing to live with a significant amount of overhead, both in storage and in bandwidth, in order not to violate this principle.
The backup box, of course, could push encrypted data to untrusted storage, such as S3. But only after it has pulled from the original box. In both cases, the connection is initiated from the backup box, not the other way around. The backup box never accepts any incoming connection.
Does Attic support this kind of use case? The documentation doesn't seem to have anything to say about backing up remote files to local repositories. I don't see any reason why it won't be supported (since rsync does), but "nominally supported" is different from "optimized for that use case", and I suspect that many of the latest generation of backup tools are optimized for the opposite use case.