This post is mainly for Sampson.
I gotta say, since this list places more emphasis on skill, and less on "importance", I think Tony Williams could move above Gaye, and probably Cooke too (Sam only beats him in influence and phrasing).
Hell, if it were up to me, I'd put him at #2 probably.
I say this not as a fanboy of Tony, but he totally KILLS in each of these criteria you've established. I'm not sure how well-versed you are in the technical aspects of singing, but Tony was one of a kind.
His dynamics are absolutely incredible, probably even on par with Jackie. Few singers of his era could transition from soft-to-loud (and loud-to-soft) like he could.
Phrasing. His melodies are to die for, especially the way he does those little soulful flourishes in some songs (like Cooke always did).
Power. Now THIS is where he really excels. Like Jackie, again, he had an immensely resonant, operatic belting style. And when he let loose, it's like you could almost feel the ground shake beneath your feet. Listen to his version of You'll Never Walk Alone if you doubt me.
Versatility. I haven't heard all of his discography yet, but so far he definitely seems more versatile than Gaye and Cooke (not Jackie though, as JW was the most versatile soul singer of them all).
Emotion. Obviously it's subjective, but this is his strongest asset as a singer. Again I mention his version of You'll Never Walk Alone. I've heard four other versions - Elvis, Jackie, Roy Hamilton, and the Righteous Brothers - and Tony's version stands head and shoulders above them all. It moved me to tears.
Range. Obviously, his range speaks for itself. He could belt up into the upper 4th like it was nothing (probably into the lower 5th octave too).
Influence. This would be the only area, imo, where Cooke and Gaye would beat him.
Anyway he is just the PERFECT r&b singer to me. Never a wasted note, every word is always sung with meaning and passion.
Plus being the lead singer for one of the 5 most legendary vocal groups ever is certainly a little bonus.