So just a quick update for those who happen to stumble upon this thread with the same issue.
In my last reply to this thread, I concluded that the issue was related to an electrical issue in my home, because I could not reproduce the issue in another building.
Since then, I took the setup to 2 additional houses (lots of lugging equipment around!) and was able to replicate the issue both times. So, I ended up sending the iMac back to B&H, and I received a new one. Lo and behold, the awful cyclical clicking noise is gone! Hallelujah! So the issue was with the machine itself.
This new mac does produce a tiny bit of buzzing noise throughout the circuit, but it is only audible when my amps are CRANKED. And it isn't an awful clicking noise, it's a slight buzz that goes in and out depending on the usage of the computer. It isn't a dealbreaker, but I am going to try out the [Invalid or Expired Link Removed] to see if I can clean up this last bit of noise. Not sure if this is a snake-oil-esque product, but I'll let you all know how it works out.
Thanks for the help everyone!