I've fixed this now, but I've left it here so other suffer less - the fix is to turn of "Use Cached Exchange Mode" under Account Settings.

Symptoms:

If I send an email to an internal person@school email address, it works fine without issues.
If I send an email to an external person@otherdomain email address, Outlook 2007 freezes after hitting "send" and I eventually hard kill it.
On restarting Outlook, it happily sends the email from its Outbox.

So far I have:

Run outlook with the /safe switch
Deleted the profile
Deleted the mailbox
Removed AV
Installed different AV
Deleted RSS feeds
Turn off "generate exchange views"
Checked DNS to ensure everything resolves correctly internally for AD and externally for the destination domain