I would like to backup offline a Windows EC2 EBS Volume, i.e. on my computer and not in the cloud. Note I can stop the instance and detach the EBS volume if needed.
Is it at all possible with Amazon's toolset, and if not, how would you go about doing it?
Amazon's Storage Gateway system may be able to help. There is an AMI which you can launch on your account, attach the EBS drive (or a snapshot of it) to the instance, and you will be able to replicate the disk's contents on your local network via a Virtual Machine (VMware iirc).
Storage Gateway also works the other way around, that is -- replicating your data locally up on S3, fully snapshottable and accessible from your EC2 instances without having to re-download the entire snapshot.
The downside, whichever way you manage to do this, is that you still need to have available the bandwidth locally to copy the entire disk's contents.