hmmm, im sorry i hvnt read all the posts.
My initial belief is anyone who is not a uchiha is perceived by madara as a senju's clan. Yes im saying the world is limited within the two clans -senju and uchiha.
and, in manga
senju-believe life force is the way of peace
uchiha-believe power is the way of peace
senju=fire = naruto (madara said he saw senju's in naruto)
uchiha=hatred =sasuke
(in one of the conversations madara had with naruto,kakashi,yamato)
Guess the final scene of Naruto vs sasuke will be will of fire vs hatred.
although the kages became kages,some of them did not inherit the will of fire. So Senju's clan I think its part of a choice. Its more than a surname that became extinct. Anyone who inherit the will of fire through various masters,ninjas becomes a Senju spiritually. They choose to resolve by (love,passion)fire instead of hatred.
That is why Hashirama Senju(presumably conquered his hatred) was able to control the tailed beasts as his pets (though he is not a jink), and madara was wounded badly in the battle against Senju.