Unfortunately it's not going to be as simple as replacing a driver and rebuilding the application. The Nextion display works in a very different way than the normal displays most people use for microprocessors like arduino and teensy. Normally the display is a "dumb" device that just handles displaying the dots. Software libraries are used to provide basic functionality like drawing lines, boxes, and text. Touch events are handled completely separately by other libraries.
The Nextion display is the opposite. The display has it's own microcontroller, memory, etc. and the arduino communicates with it through a serial interface. All of the buttons, text, gauges, etc. are prebuilt in the Nextion editor. The application doesn't know where they are on the screen. It just has a name such as "button1" that is associated with a button on a particular screen for instance. The application just sends a command to the display to change the text of "button1" to "abcd". It would require a significant rewrite of the JackAl UI code to make it work with a Nextion display.
The other thing as Jack pointed out is about resolution. The Nextion displays most people have are much lower resolution than the display used by the JackAl board. The 2.4" and 2.8" Nextion displays are 320x240. The 5" Nextion display ($60) is the closest one with similar resolution (800x480) and that is 33% more in price than the display ($40) that JackAl currently uses. Even the 4.3" Nextion display is only 480x272.
Brian - N8BDB