Fixed! Not completely sure why, but switching:
$mail = new WireMail();
to this:
$mail = $this->wire('mail')->new();
in the LoginRegister module did the trick — line 684. Now Gmail's sending my registration emails too ?
Gotta say, I am hugely grateful for Processwire. Ryan, and all you fantastic moderators and commenters—this is such a great place to learn, and goddamn if the sky doesn't seem to be the limit.