I didn't have quite as much time as I was hoping to work on Display Squared this weekend, but I did get this CAD proof of concept finished in time to submit this project the the 2021 Hackaday Prize. Below you'll see the current mechanical plan for this project.
The ruby red cylinder is my pressure vessel. This is the container that I'll be varying the height of to extrapolate pressure using Pascal's Law. That pressure vessel has a quick-connect tube output that leads into the Solenoid Valve. The Solenoid Valve will be controlled by an Arduino, and it will open and close to allow water to flow out from the output nozzle. The solenoid valve and output nozzle assembly is going to be actuated along the Y Axis with a simple stepper motor, GT2 belt, and linear rail configuration. Here's a shot of what this is all going to look like from the front.
Now I just have to get to making these parts. This CAD is far from finished, and I'm mostly looking to put enough of this assembly together to do a quick sanity check on my math from the previous build update.