Downloading SRA Files from AWS
A member of the SRA submission staff pointed out that using

prefetch --type all SRR5253957


will download the original files. In this case, it means running the above within an EC2 instance colocated with the S3 bucket (so, us-east-1) and having installed and configured SRA Toolkit to work from AWS (as per this documentation).

Unfortunately, the particular files I am concerned with are not currently accessible, but this should generically work in most situations.