Lookup what's the email host of the destination address. Get a local account on it. If the provider supports scheduled sending, use that, otherwise use Telnet or automate the HTTP request to the webmail.

Being on the same provider will remove a lot of the variable delays in internet delivery. Scheduled send could also mean your email actually arrives in the destination inbox ahead of time but is just hidden until the required time (as it may all be one database under the hood).

If you can get 2 accounts on said provider, you can also test various strategies against your own accounts.