So long and short Xenforo was eating its self in email. I'm not sure what started the loop but the xf_mail_queue database table ended up with 46GB worth of duplicate emails stuffed inside of it. Because it had so many emails, and more getting added for every forum post / registration etc it could never complete an entire 'send'. I've had to manually purge these emails. After that I registered a test account to ensure emails are functioning properly & that the email queue is purging itself as it should as well which it is.
We're now showing a proper empty xf_mail_queue and no new errors logged within Xenforo.
Looking more towards the root cause, my best guess is we hit some weird Xenforo bug which caused an enormous amount of duplicate emails to be generated and it was either triggered by/during the migration or from the SMTP failures. I'm not sure why it would have hit such a condition, as looking at things this should have been only a few hundred emails impacted at most, not thousands like it was. The emails not working were obviously bad, but that's where the problem should have stopped, and when that fixed it should have just sent the couple hundred back-logged.