(thanks guys - this is my first posting ever...so forgive any breaches in Adobe ettiquette
Thank you for a rare interesting post.
I'd come at it from another direction. Rather than move tiny bits around the screen using dozens of layers, just use two or three layers, and create the sections in the layer mask.
Open your master image and create a new layer. Make a rectangular selection and fill with black. copy that layer, and offset as below, and merge the two layers
Drag a selection around the above rectangles, and with other layers turned off, Edit > Define pattern. Turn this layer off.
Make a new layer and fill it with the above pattern. Use Free Transform to make the pattern fit the screen nicely. Turn this layer off
Turn your portrait layer on, > Ctrl (Cmd) click the pattern layer, and add layer mask to portrait layer.
Copy this layer, and invert the layer mask.
Unlink the layer mask, and make sure the layer icon is selected, and not the layer mask.
Offset this layer. The portrait will move, but the layer mask should stay in the same place.
Repeat above steps experimenting with layer mask inverted, and not inverted.
The layers panel will look like this:
And image like this
It took me longer to write this post than create the image above, so with time and thought, you can make something much better. The point here is that it doesn't have to be a ton of work.
Good luck, and try and remember to show us what you make.
Looking at your example some more, I'd definitely be inclined to place some guides before making the pattern. You'd need to make sure things fit from the outset though, so go View > New guide > Horizontal 20pc and repeat with 40pc, 60pc and 80pc. This will give you horizontal guides at 20%, 40% etc.
The point of the guides is that you will be able to accurately drag selections around groups of rectangles to firm up areas of the finished image. Like to give back focus to the eyes.
Your example is actually a sort of segmented triptych with three views of the subject merged with the segmented masks. I would make a reasonably detailed plan before starting such a project, so I could get the right things in the right place - like having eyes, with some looking space, appear in the best position.
You could also use the same layer mask in adjustment layers to produce darker segments. Another reason why guides would be useful.