Install flashme and make sure to use a non-insulated tool to short the circuit. It will definitely black the top screen. That is the only real good idea I have, because having a homebrew loaded that would black out your top screen would mean you have nothing else but that homebrew running. Apparently, ANY solution that we could possibly tell you would involve covering the screen with something because there is NO alternative. Disconnecting the top screen will result in a non-functional unit, but if you want that, go for it. It's either you listen to our suggestions and put something over the top screen or just deal with it.
Also, what sort of strange conflicts are you having in your head :/...You have a top screen that is giving you issues and thus you don't want to see it, but you are not willing to cover it with electrical tape because it will ruin the screen protector for the screen you aren't intending to use anyways and/or possibly already bear with the problem otherwise in order to utilize the top screen in the first place.