"Aiki as ura of kiai." This formulation is Mochizuki's - and further, kind of common in aikido circles. But it is not general, and is kind of a "throw-away" line, to attempt to distinguish "aiki" from kiai, a concern of aikido folks more than any others, and comes from a limited understanding of kiaijutsu.
Ellis, an interesting comment, but I have to say I've never heard that definition from any other aikido teacher or group.
Second, I wouldn't think it really comes from a limited understanding of kiaijutsu because Mochizuki Sensei was a hard-line karate man as well as a swordsman and he did believe in kiai. He didn't think you could have aiki without it. So it had to be developed. He defined aiki as the ura of kiai when I asked him to explain aiki. I think it was at that same time that he saidthat if one has aiki, he does not shrink back from a surprise attack but attacks the attack. But he attacks specifically the ura of whatever attack form the attacker uses--be it a kick, punch, sword strike, whatever.
I think it would be mistaken to characterize him as having a limited understanding of kiai/kiaijutsu.
Much more common in koryu is a more sophisticated and detailed delineation of kiai, using gogyo (five element theory), for example, with variations of yin/yang, etc., association of kiai with seasons, body parts, etc.
Almost everything in human life is basically "kiai" oriented. You mention very specific and rather esoteric examinations of kiai (gogyo, yin/yang, etc.) that do seem to come directly from the Chinese. But these are esoteric refinements of what is effectively the omote
of human life.
Aiki is the ura of all
of that--the ura of everything.
And as for being able to affect the mind and body of the opponent at a distance, remember Takeda's statement that aiki overcomes the opponent mentally, at a glance, to win without fighting.
It may be a throwaway statement to say that aiki and kiai are omote and ura, but the fact that they are is worth deep consideration.