I’d like to send kudos and thanks to @Arkshine for assistance thus far. Apparently the VPS cannot reach the hosted domain - hence the mails don’t work. That’s pretty weird, but I’m contacting the hosting provider to check on it. Will update.
That was pretty quick and easy. A simple ping to the hosted domain from a SSH session to the VPS running Discourse showed what was up. Let’s see how it goes.
EDIT
Kinda wished @Arkshine had replied so I could mark that as the solution. Anyways - heard back from the hosting provider. Apparently their servers automatically blocked the VPS IP due to failed attempts of SMTP. Not sure what was up with that - will change settings and run tests again and see. Should be good now - hosted IP is pingable from VPS now. Tested email settings and we’re good to go!
Hopefully this info helps someone. If I could edit the OP then I’d just put in a TLDR - or they can just click the link to go to the solution.
Again - many thanks to @Arkshine for all the help. Keep up the good work!