Hey Nick. Thanks for reaching out and welcome to the community!
Do we go with a similar video over ethernet solution that has more expandability to get rid of multiple devices doing one job or do we go with something like an SDI matrix like the Blackmagic video hub? What are the pros and cons of each option and is there other/better options that I'm missing?
First of all, I almost never recommend running uncompressed video over Ethernet or Cat 5/6/7. Category cabling was not designed to carry uncompressed video signals, especially over long distances. Over the last decade I have seen a vast majority of signal issues coming from HDMI over Cat 5/6/7 extenders.
The only time I recommend using Category cabling to distribute video is if it's done with solutions like NDI or SMPTE 2110. Those compressed IP solutions are designed specifically for professional broadcast applications and can be excellent for distribution like you're needing. They give you greater flexibility for routing and are easily adaptable, but they will end up being more expensive to do correctly.
If you can setup a solid NDI system then that would be the most versatile, allowing you to basically route anything to any display at any time.
Otherwise, I would suggest setting up a solid SDI infrastructure with a broadcast SDI router (not quite the same as a matrix in many cases, so keep that in mind). The router will essentially become the main "hub" for your system. By running all you ins and outs through a centralized router you will have the ability to control every source and destination in your system easily.