Got off the phone with MT. Here are some new things I'll be trying.
We don't cover support on Let's Encrypt SSL's unfortunately but we do provide a detailed guide on installation that will hopefully guide you through by successfully securing your sites with their services.
Install a Let's Encrypt SSL | Media Temple Community
This also seems to be pointing that it could be a temporary issue from within Let's Encrypt's Servers:
DNS query timed out - #11 by jpbe
Also googled about Plesk + Let's Encrypt and found the following:
I will also be trying simply temporarily re-creating my current DNS setting back at GoDaddy to simply get past the problem and move on with my life for the weekend.