Apparently this just isn't possible. I've used the core portion of the second bit of code in a few other questions and know it works, but there's a hitch. In those questions we were setting the send through account when the item was created, not in the sending process. Having used the code before and knowing that it works I didn't bother to test it before posting. Apologies for that. It appears that Outlook just won't allow us to change the sending account when the item is being sent. The only solutions I can see are to select the sending account when creating a message, or have multiple send buttons that send through different accoutns.
