This does appear to work. I've added some sample code:
const MAX_MOUSE_SPEED = 25
func _input(event):
if event.is_action("ui_axis_up"):
Input.warp_mouse_pos(self.get_global_mouse_pos() + Vector2(0,-MAX_MOUSE_SPEED * -Input.get_joy_axis(0,1)))
That seems to function, albeit not smoothly yet, but I think I'm on the right track. Thanks!