I think you are missing something, though I can see why it wouldn't be obvious. Although the READER partition is part of the devices internal storage, the reader itself doesn't view it as internal (it's even mounted as /mnt/sdcard)
Basically when any Android device says there's not enough 'internal phone storage' it means the /data partition is getting very full. This is the partition where apps are installed by default.
One way to free up space might be to enable apps2sd, which would allow you to move some apps to READER partition and thereby free up space on the /data partition.
Also see:
https://wiki.mobileread.com/wiki/PRST...space_for_apps