This is only theoretical, as I'm a dualsticks guy and don't use the touch controllers for elite, but I can see no reason why the axis' from the thumbsticks couldn't be ran through"joystick curves" (a program I'll post a link to and a video tutorial for at the end of this post). In case you aren't familiar with it the program is used for adding responsive curves to joystick axis and the way it works is takes your joysticks input from direct x, processes the signal against the curve you've plotted for the response, parses that to vJoy which creates a virtual emulated joystick device and passes its signal to the game.
Can be a bit of a pain to set up but putting pitch curves on the joysticks would effectively solve both of your problems, as by lowering sensitivity around centre would mean that when rotating left or right if you did slightly encroach on the y-axis the response from the ship would be a lot less pronounced. And having those curves would essentially reduce sensitivity, while allowing full stick to mean full axis input.
https://www.xedocproject.com/joystickcurves.html
[video=youtube;CqzoJPCZM0w]https://www.youtube.com/watch?v=CqzoJPCZM0w[/video]
And another thread from this very same forum mentioning it already:
https://forums.frontier.co.uk/showthread.php/404948-How-to-configure-joystick-curves-for-dummies