I think I may have figured out the cause of the problem: It may be because I was creating multiple ID3D11Device for the same Adapter.
My code was overly complex for what I needed as I was following techniques introduced in this article when I really didn't need anything more than a single thread for all windows and rendering. After sharing the same ID3D10Device for each Render Target (one Render Target per Output, one ID3D10Device per Adapter) I have successfully got DXGI with DX10 rendering two full screen displays as shown in my rough memory-leaking proof of concept.
Since this was my first time working with any of this tech, I used this article to help me along with this process: Display Different images per monitor directX 10