Objects moving in front of screen replacement.

I am pretty new to Fusion and I am working on a project in which I have to replace a few computer and phone screens. I've figured out the screen replacement well enough using the planar tracker and corner pinning, but I have a few moments where actors partially block the screens with parts of their body or their hands.
What is the best way to go about masking out the covered portions of the screen so the actors remain in the foreground and don't suddenly seem to magically disappear behind the screen?
And btw NO, the screen replacements were not done over green screens, just blank black screens, so the chromakey thing is not an option. Many thanks in advance to anyone who can help with this!

I know one way to do it would be to use Rotoscoping, use a polygon mask and mask out the object you want visible.