So, here is what is done better explained with a quick sketch of the mod performed. Skecth is just for illustration, it is not a working drawing...
The top of the case is shaved slanted: looking at the drawing you will understand why I believe it is the best option.
Shaving it flat can't work as we can't modify the inner part of the case on a budget as that would imply very expensive works that would exceed the price of a Vietnam made case. And the point here is to stay a