So after scouring The Division subreddit and finding out that it either came down to server issues after recent updates, or it was my system being "bottlenecked", I decided to take matters into my own hands and give my system a proper cleaning and upgrade.
I pulled out my 5 year-old CPU heatsync and fan, which was a Zalman CNPS9900MAX-B, and replaced it with a Corsair Hydro Series H50. The Zalman was advertised as a "long life bearing fan", and while I am not disappointed in its performance over the 5 years of ownership, I'm not entirely sure 5 years qualifies as being "long life". I did notice (and recently pointed this observation out to my wife ( @reptimom88 )) that the fan in between the heatsync of the Zalman began to make some rattling noises. I'm not sure how long this has been going on, but I would suspect it began within the year.
Since swapping the old in with the new and giving the ole' PC a decent cleaning, I decided to try doing something I had never done before; overclocking the CPU. Sure enough after some minor trial and error, I managed to overclock my ole' Core i5-3750K processor from 3.8Ghz to 4.0 with no issues, and believe me, that doesn't seem like much right off the bat, but when I loaded The Division and started sprinting down the street at optimal graphics settings with no hiccups, I almost cried.
So, hopefully this holds up until I build a new rig in the short future. And hopefully this fixes the "dropped frames" issue we've been having in OBS. But with that I shall say it was a successful upgrade to our #streamlife!
I wish for many upgrades in your #streamlife sooner than later.