Can I ask how you fixed it? I believe I'm having the same issue you were. My textbox is still showing behind the phone UI. It's happening even with the readme snippet applied.
No problem !
If I remember well, I re-installed the screen part from scratch, copy/pasting everything from the Renpy Phone game and adding my custom elements after it ! I also checked for any part that might have been in double ! Hope you can fix this issue too !
I also discovered the textbox might stay if you write some messages before the reset variable (I used this in order to do a teasing scene, and then resetting the phone at the introduction part so the first messages were erased).
I hope you'll succeed in fixing this too ! Good luck !