FYI, DigitalOcean is rolling out expandable block storage summer 2016 (so any day now), so that might be a good way to go. Not a lot of information, but keep an eye on https://www.digitalocean.com/features/storage/. You may be able to ask support to manually add you to the beta if you need it right now. DigitalOcean is really good about going out of their way to win your business. Full disclosure: I have no relationship to DO other than being a happy customer.
If you're looking at mostly static assets though, why not just upload them to S3 and serve them directly from there (or via a Cloudfront distribution)? EC2 boxes are fairly inexpensive as well, and there's all kind of automation tools for provisioning your AWS resources + configuring them.
+1 on DigitalOcean with Block Storage. Currently using DO with Amazon S3 mounted using /etc/fstab via S3FS https://github.com/s3fs-fuse/s3fs-fuse (which has eventual consistency but if you want cheap)
If you're looking at mostly static assets though, why not just upload them to S3 and serve them directly from there (or via a Cloudfront distribution)? EC2 boxes are fairly inexpensive as well, and there's all kind of automation tools for provisioning your AWS resources + configuring them.