Turns out that the CNAME that you need to apply to your domain to allow Amazon to sign your emails uses something like this:
**************._domainkey.your_domain.com (where ******** is some random text).
Unfortunately, older versions of Plesk will not allow you to enter the '_' (underscore) character - the reason is just plain boring, so I won't explain.
However, if you have access to the database which is running Plesk - the PSA as it is known, then you have a work around:
https://forums.aws.amazon.com/thread.jspa?threadID=122844
This worked for me and Amazon took about 30 seconds to auth my domain once I had carried out the instructions contained in that article.