Hi All, thank you all for the comments. I think threads like this are the useful type because they provide a problem and solution. In my case I always like to provide as much of a solution as I can offer. I always learn a ton from posts like this across the many forum communities I engage with and love to contribute back.
I went about cleaning the clog using a heat gun as @gr5 suggested. It mostly worked as it was the only real way to separate plastic from printer parts. I ended up using several types of pliers and snips to cut away plastic as I went along. Overall the cleanup took about 4 hours and resulted in losing the two print cores. I really tried my best to save both cores down to the end when I discovered they were stuck within two rings of plastic in the bottom metal plate (just above the white silicone sheet where the nozzles stuck out). They broke just between the extruder block and the aluminum shaft with threads. You can see where they broke in the photos.
I got to this point by taking apart the entire extruder assembly and removing the two axes. I didn't expect I would need to remove as many parts as I did. As a result I am now wondering if there is a better solution to this problem. Meaning, I wonder if there could be a better design for the the dark grey plate (shown in UM-Issue-12.jpg) that holds the black base of both print cores such that in the event plastic comes up to this point due to failure, it would not be able to get stuck inside this region inside of the print cores (UM3-Issue-11.jpg)? What if the dark metal piece doesn't have sunken wells for material to get stuck in? Would this change anything else in the system design?
I'm currently out of commission still but will look into @SandervG's advice. We have only had the system for a few months so I assume it should be under warranty. I'll report back on this later.
In related matters, I attempted to install one new AA print core and use the machine with only 1 core. I am finding that that the printer will not respond to only 1 print core being installed. It apparently requires two to be installed. I found this post about Cura with an interesting response from "Ghostkeeper" about using the printer with one print core. I'll repost the response below.
Hopefully this helps others that may encounter this problem in the future. Cheers!