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MakerBot Print is our newest print-prepration software, which supports native CAD files and STL assemblies,
allows you to interact with all your printers via the Cloud, and many other exciting new features.

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Looks like a cool set up as it is. You could just drill a hole through the top and print a mount for the ts with the cable going into the existing box through the top, something like this (the center part)
https://www.thingiverse.com/thing:2600591

This is also really cool looking and may check some of the boxes:
https://www.thingiverse.com/thing:2748195

Were you planning to use a t/s that connects with the flat cable? I was thinking of buying one of these for my printer, and it uses HDMI and USB so cable length would not be a problem (could be moved remote from the control box):
https://www.amazon.com/Kuman-Capacitive-Display-Raspberry-SC7B/dp/B01F3801A2

Squeeze Pi Enclosure
3D Printer Electronics Enclosure - Touch Screen, Mainboard, MOSFET, PSU, Raspberry, Fan.