Hi Scott,
It looks like you have a rather exciting project in mind and as ieee488 has mentioned, it is definitely doable.
The implementation ieee488 has described works great for a basic LCD module, and you can see an example of how that might look, complete with code, in the Arduino Intelligent Series I2C Application Note we have published here.
If you’d like to implement a similar menu on a full colour TFT module, you can take a look at the GTT29A Demo Design that was created with display Designer Software. For more information regarding using this type of GTT display, check out this post on the forums.
Please keep in mind that I do represent Matrix Orbital and can full support every one of our products, but all of the links provided here are to free resources that you can use to develop your own project on a display of your choosing.
Cheers,
Troy