>and as long as it does not degrade server performance I'm A-OK with it.
No, this should be fine. As long as gmail is happy with your emails (SPF, DKIM (in version 78 of WHM / cPanel) and DMARC) it shouldn't ratelimit / block the emails.
>how much door knocking (number of log-lines in...
Email headers are read from the bottom up. Here's the culprit.
Received: from [18.104.22.168] (unknown [22.214.171.124]) by vps29.xxxxx.com (Postfix) with ESMTP id 8A1562560208 for <TKitten@twitchinkitten.com>; Mon, 27 Jun 2016 10:16:59 -0400 (EDT)