Hello,
Unfortunately the fact that you found a 2FA plugin is not helpful to me. To implement a 2FA solution, the hard part is actually integrating it to the plugin, not finding a plugin that already uses such a solution. Thanks for the suggestion, I might implement it later if I find some time, however for the time being I would recommend that you work on your email issues. There is no reason why sending email should not be reliable. As you said, using an SMTP plugin might be a good idea, if the default mail capabilities on your server are not correctly setup. The one I’m using is https://wordpress.org/plugins/wp-mail-smtp/
thanks