I'd definitely consider using Amazon Cloudfront as a CND first and then do additional minification as needed. I think that serving assets via a CND will give you bigger boost in performance than just minification.
Additionally, Assets plugin for Expression Engine has a built-in Amazon S3 support so it could make syncing your assets with seamless. Alternatively, you could rsync
periodically, that works well too; I have used s3cmd tool in the last it works well (don't get turned off by the look of their website, s3cmd is very easy to use.