I worked on this for about a week prior but didn't make a project. A lot of it was working on software, which now works pretty well. Then, I started modeling a backplate since the LED matrices have very convenient hole patterns around their perimeter that I figured I could hook into.

After some back-and-forth, I got the hole pattern correct in Fusion 360 and printed out a central plate that holds the two matrices together. There are some adjustments that need to be made regarding peg length and angle but it works well.