I agree with the first part of your answer, Kent, in that you can go from org. to org. and find plenty of differences being taught, all 'handed down from the Founder'.
I disagree that kicks, punches, etc being taught or being used absolve you from a moral factor, and would say that is the difference between what looks like aikido that is being taught in Judo, BJJ, Karate, etc. For instance, the kick or punch done as you described earlier might have been to demonstrate openings that are left if a tech. is not done correctly (kick with kotegaeshi) or as an attack (the first you mentioned)...I have been in a class where Saotome Sensei made us just do punches all night, but his explanation at that time was we punched too ineffectively to practice technique against.
Futher, punches and kicks can be integral parts of a tech., either as atemi or another part, but it is the spririt that it is delivered (and perhaps the timing) that makes it different. Are we pucnhing/kicking to maintain space/move our attacker, or are we punching him or kicking him during the pin (I've seen this taught in aikido dojos, but to me, kicking someone after you've subdued them is not aikido).
I of course can have it all wrong, but it is easiest for me to connect to my pertner, especially those I'm not personally fond of, if I make an active attempt to truely see them, as my fellow human, as a person trying to improve, and if there are problems in our interaction, to look at why he may be acting as he is, and at all times, no matter what is transpiring on the mat, to make sure I protect my uke to the best of my ability.
Aikido-looking techniques, when they've been done to me by people who either by my observation or dojo opinion are a bit antisocial (unable to see humanity in others), feels quite different.