No one group "bare the most relation." Each dynasty is unto itself. The Nuba people aren't Cushytic but were just as instrumental, same as Interior Africans coming from the West as the Wet Sahara dried or the Nilo-Saharan/Chadic farmers from S Sudan.
So you're saying the ethnic make up of Egypt drastically changed each dynasty ?
And I agree that there will never be a definite way to determine which group are most related to AE's, but I think it's fair to say those from that region and part of the afroasiatic/Nilotic family do so more than other ethnic groups in Africa Breh.