As Flav said, we got controls working by using the controllermap utility included with SDL2.
HERE is a good guide on getting an initial version of the controllermap working, but you will need to plug in an external keyboard so you can skip the buttons you don't want to bind. Bind all the keys, and put the output config line into the controller file at ~/.lexaloffle/pico-8/sdl_controllers.txt. If you already have the system in emulationstation then you should only need to open Pico8 and rebind the keys as you want!
Our config looks like:
15000000010000000400000000010000,GPIO Controller 1,platform:Linux,a:b3,b:b0,x:b1,y:b2,back:b6,start:b7,leftshoulder:b4,rightshoulder:b5,dpup:-a1,dpdown:+a1,dpleft:-a0,dpright:+a0,
Yours may vary if you are using an older version of the joystick driver or the old tact switch button layout.