Would you believe it.
I have put in the exact same data and options and it works now.
RE: ...smtp: The SMTP server does not support authentication.
That seems odd if you are "using Port 25 with neither 'Use SSL' or 'Use default credentials'"
I have realised it’s an hosting error, something to do with the server not allowing external connections.
I configured NopCommerce to use their proxy so keep alive now works, but I believe either the sending emails doesn’t use the proxy or the proxy is having an issue with the smtp servers.
Last night I cancelled my hosting plan, and tried another provider and it all works now