"Extending ki beyond the limb" sounds perilously close to ki ball demonstrations and knocking people off their feet from 10 feet away, although I'm sure you are referring to something else entirely. For example, there are times that when I uke for Mary I'll say to myself "this is a really bad idea" before we ever make contact. I will feel something in me, not a force acting at a distance, but a feeling of unease and my impression of her will be one of a person taller and more imposing than she is normally. What I am experiencing in that moment is an extension of her ki, which is the result of her coordinating mind and body to a very high degree. I used to have the same feeling whenever I was uke for Maruyama sensei.
I don't view ki as a flow through a channel. I see it as a result of mind and body being tightly coordinated and highly focused. It's more than body organization, it's about the organization of mind and body. And once ki is manifest it can be manipulated via intent, to the extent that it can be felt across a distance by uke.
Although one talks a lot about projecting ki in (Tohei oriented) aikido, I've come to see ki more like a substitution/synonym for an interface of vitality between mind and body, whereas intent now is the thing to be projected. For the time being, as is.