Oh my god.
I agree that binary search won't lead to the answer, but it seems like ideas and theories are getting lost in the noise of the general thread.
We have an entire board that we can utilize, where threads don't get pruned. If we're looking for the hidden relationship to unite this thing into one functioning piece, we can make progress by dividing and conquering the problem.
So, we make 5 threads. One for E, F(-E), N, D, X. We look at specific values which cause strange behavior with other values. For example, E58. This is the least populated E in the entire grid. Why? because E58 has an absolute fuckton of primes and coprimes in it. But why E58? What can we learn about the rest of the grid through E58?
N for example, where N is prime, the populated cells have significantly less values. Why? What insights can we gain by breaking this grid into the smallest pieces? What formulas can we create to relate variables to other variables? Can we understand how every little tiny piece works and bring it back together when we're done?