@Vlad-Nirky Hmm, not sure. Running adb root for me gives error message adb: unable to connect for root: closed, but I can use sudo inside adb shell: using that would probably let me get a step closer, by allowing me to copy data to an SD card for instance. The problem is my computer isn't an adb client so I can't just use my phone as a host and run adb root on it.
Going back to the module installation, I should definitely look into that, as it sounds better than the whole hassle of the SD card (which funnily enough is one of TWRP's limitations).