I don’t know the answer, but I can try providing a few pointers…
We have a class called SugarPHPMailer which is a wrapper for phpmailer and which, even though it is still not upgrade-safe, is always a better place to customize. At least it’s not inside 3rd party code, like include\phpmailer\class.phpmailer.php.
If I were you, what I would do is
turn on some logging here and make it fatal to ensure it gets logged
set show_log_trace to true in config_override.php
now get one of those emails to send (make sure it’s form a meeting invite) and check the log trace to see the entire call stack. Try to make your intervention as far up the stack (earlier) as possible, especially if you spot a file that is customizable in an upgrade-safe way.