That looks like you want to avoid simultaneous x & y motion. An advantage of GRBL is that it can do coordinated x&y motion in straight lines at an angle while also doing smooth acceleration. That's tough to do with the standard libraries. If you don't want coordinated movement with, and can settle for individual axis movement at a time, then it's much easier.
Regarding the joystick motion-- would you want that to work much like the buttons as sort of an on-off (digital joystick)? Or do you want some analog action so that if you push the joystick farther it moves faster (analog speed control) or farther (analog position control)? If it is like a digital joystick, then perhaps it could work exacly like the buttons and be wired up in parallel with the buttons.
The Mobatools library examples are the richest examples I've seen, with "Example 3" sounding close to a 1-axis example of what you are describing, and might be easily extensible to two axes.