I'm posting the outcome of my situation so that going forward, hopefully it helps someone with the same problem who is doing a Google search.
After talking to the maintenance mechanic at my employer, he recommended that I put a compressed air hose on the drain tube to see if I could blast whatever was clogging it out of there.
So here is what I did:
1) Because of the location of the tube, no need to jack up the vehicle. It's easier to reach from above. The location of the tube is on the back firewall just to the right of and slightly lower than the bottom of the engine block (standing in front of the vehicle facing the engine block with the hood open)
2) There is an elbow tube attached to the end of the AC drain tube. The end looks like the end of a sparkplug wire (the end that attaches to the sparkplug) with a perpendicular black drinking straw attached to it. It just slides right off if you pull on it. I can't post links to YouTube yet. I'm still too new. But if you search the following term on YouTube you'll come up on the first video by username Chris Henderson. It'll show you what the elbow tube looks like and where to find it:
"2013 GMC Terrain AC Drain"
3) Once I popped off the elbow tube, there is a one inch black tube sticking out of the firewall that it attached to. I had one of those portable air compressor tanks and I put the end of the nozzle inside the tube and blasted it with air. After 10 or 15 seconds, I heard a small "thump" and at least 3 gallons of water (maybe more) came flowing out of the tube on the firewall.
4) I blew out the elbow tube attachment to make sure it was clear and once the water stopped flowing, I re-attached it. (it just slides right back on the 1 inch tube on the firewall)
5) I ran the air conditioner on full blast for about 20 minutes after that and so far so good. No more wet carpet and water is now flowing out of the drain under the hood as it should.
I hope this helps someone in a similar situation. I know most mechanics will charge right around $100 just to take a look at your Terrain. I will continue to monitor this situation over the next several days to make sure it's definitely been corrected.