You can temporarily "borrow" the screen from another touch. You can get ssh installed on it using tools from the "simple debricking" sticky thread in the dev corner. Then you can install a remote tool that exports the framebuffer over USB, making the kindle screen CONTENTS visible on your host PC. For the touch, there is a VNC server that runs on Xorg in the touch. There are also native mode methods that would even work in diagnostics.
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