As I understand changing crystals is a hassle to debug since reprogramming needs the original 16MHz crystal and not something for the beginner. Please tell if I am wrong here!
I think that would only be a problem with the Arduino bootloader/IDE, and probably don't want to use those. I'm not sure if the existing bootloader will work for you, but you will need a different (or heavily modified) compiler/IDE. (Just for example, the Arduino compiler doesn't have functions for keyboard/mouse input, text/graphics display, or file system access.)
What are you going to use for an operating system & compiler? That'll have to be modified to match your particular/unique hardware.
- cost < $50
Every Arduino project I've built has cost more than that... But I'm including the cost of a case, power supply, switches, connectors, LEDs, and whatever other little electronic parts I've needed.