Found some connectors that allow you to minimize the “cable bloom” as they come out of the touchscreen. There are 90 degree connectors for both USB-C and mini-HDMI that route the cables immediately to the rear. My cables now only extend 3/4-inch from the side of the touchscreen.
Update - Should have noted that these connectors are modular so you can just add them to end of existing cables. The USB-C 90’s are by AGVEE and the mini-HDMI (to full HDMI) is by CableCreation. Both are available on Amazon.