Dear Paul, thank you for your help! I only saw this much later. I have now set up Mandrill as you suggested, and now the verification e-mail works! I’ll mark this as resolved.
(I suspect the problem was related to my hosting company’s somehow not allowing the sending of certain kinds of e-mails, the kind that Simple Security Firewall needed. It was just so strange that it would allow me to send my test e-mails without any problem, but, oh, well, Mandrill solved that issue!)
However, 2FA is still not working, owing to a new problem…but I’ll post a new thread about that.